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mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Cambria; mso-hansi-theme-font:minor-latin;} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1027"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--> </head> <body bgcolor="white" lang="EN-US" link="blue" vlink="purple" style="tab-interval:.5in"> <div class="WordSection1"> <p class="MsoNormal"><span class="SubtitleChar"><i><span style="font-size:18.0pt; mso-bidi-font-size:16.0pt;line-height:110%;font-family:Cambria;mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin">Applied Mathematical Programming</span></i></span><span class="SubtitleChar"><span style="font-size:18.0pt;mso-bidi-font-size:16.0pt; line-height:110%;font-family:Cambria;mso-ascii-theme-font:minor-latin; mso-hansi-theme-font:minor-latin"> <p></p></span></span></p> <p class="MsoNormal"><span class="SubtitleChar"><span style="font-size:16.0pt; line-height:110%;font-family:Cambria;mso-ascii-theme-font:minor-latin; mso-hansi-theme-font:minor-latin">by Bradley, <span class="SpellE">Hax</span>, and <span class="SpellE">Magnanti</span> (Addison-Wesley, 1977) <br> </span></span><span style='mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><br> </span><span style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height: 110%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>This book is a reference book for 15.053, Optimization Methods in<br> <span style="mso-spacerun:yes">��� </span>Business Analytics, taught at MIT. </span><span style="font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:110%"><p></p></span></p> <p class="MsoNormal"><span style='font-size:11.0pt;mso-bidi-font-size:12.0pt; line-height:110%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'>To make the book available online, most chapters have been re-typeset. <p></p></span></p> <p class="MsoNormal"><span style='font-size:11.0pt;mso-bidi-font-size:12.0pt; line-height:110%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'>Chapters 6, 7 and 10 were not,</span><span style='font-size: 12.0pt;line-height:110%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'> but are still available (as direct scans of the original chapters). <br style="mso-special-character:line-break"> &lt;![if !supportLineBreakNewLine]&gt;<br style="mso-special-character:line-break"> &lt;![endif]&gt;<p></p></span></p> <p class="MsoSubtitle"><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt; line-height:110%;mso-fareast-font-family:"Times New Roman"'>Downloads of the book and its chapters <p></p></span></p> <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAppliedMathematicalProgramming.pdf" target="_parent">Entire Book</a><span style="mso-spacerun:yes">�� </span>minus Chapters 6, 7 and 10<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-01.pdf" target="_parent">Chapter 1</a>.<span style="mso-spacerun:yes">�� </span>Mathematical Programming:<span style="mso-spacerun:yes">� </span>An Overview<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-02.pdf" target="_parent">Chapter 2</a>.<span style="mso-spacerun:yes">��� </span>Solving Linear Programs<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-03.pdf" target="_parent">Chapter 3</a>.<span style="mso-spacerun:yes">��� </span>Sensitivity Analysis<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-04.pdf" target="_parent">Chapter 4</a>.<span style="mso-spacerun:yes">��� </span>Duality in Linear Programming<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-05.pdf" target="_parent">Chapter 5</a>.<span style="mso-spacerun:yes">��� </span>Mathematical Programming in Practice<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-06-scanned.pdf" target="_parent">Chapter 6</a><span style="mso-spacerun:yes">��� </span>(scanned).<span style="mso-spacerun:yes">�� </span>Integration of Strategic and Tactical Planning in the Aluminum Industry<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-07-scanned.pdf" target="_parent">Chapter 7</a><span style="mso-spacerun:yes">�� </span>(scanned).<span style="mso-spacerun:yes">�� </span>Planning the Mission and Composition of the U.S.<span style="mso-spacerun:yes">� </span>Merchant Marine Fleet<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-08.pdf" target="_parent">Chapter 8</a>.<span style="mso-spacerun:yes">��� </span>Network Models<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-09.pdf" target="_parent">Chapter 9</a>.<span style="mso-spacerun:yes">��� </span>Integer Programming<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-10-scanned.pdf" target="_parent">Chapter 10</a><span style="mso-spacerun:yes">�� </span>(scanned).<span style="mso-spacerun:yes">�� </span>Design of a Naval Tender Job Shop<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-11.pdf" target="_parent">Chapter 11</a>.<span style="mso-spacerun:yes">�� </span>Dynamic Programming<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-12.pdf" target="_parent">Chapter 12</a>.<span style="mso-spacerun:yes">�� </span>Large-Scale Systems<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-13.pdf" target="_parent">Chapter 13</a>.<span style="mso-spacerun:yes">�� </span>Nonlinear Programming<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Chapter-14.pdf" target="_parent">Chapter 14</a>.<span style="mso-spacerun:yes">�� </span>A System for Bank Portfolio Planning<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Appendix-A.pdf" target="_parent">Appendix A</a>.<span style="mso-spacerun:yes">� </span>Vectors and Matrices<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Appendix-B.pdf" target="_parent">Appendix B</a>.<span style="mso-spacerun:yes">� </span>Linear Programming in Matrix Form<p></p></span></li> <li class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:6.0pt; line-height:120%;mso-list:l0 level1 lfo3;tab-stops:list .5in"><span style='font-size:11.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FAMP-Appendix-C.pdf" target="_parent">Appendix C</a>.<span style="mso-spacerun:yes">� </span>A Labeling Algorithm for the Max Flow Problem<p></p></span></li> </ul> <p class="MsoNormal" style="margin-bottom:12.0pt;line-height:120%"><span style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'><span style="mso-spacerun:yes">����� </span><p></p></span></p> <p class="MsoSubtitle" style="line-height:120%"><span style='font-size:16.0pt; mso-bidi-font-size:12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"'>Some Excel exercises.<p></p></span></p> <p class="MsoNormal" style="line-height:120%"><b style="mso-bidi-font-weight: normal"><span style="font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height: 120%">Remark</span></b><span style="font-size:10.0pt;mso-bidi-font-size:11.0pt; line-height:120%">:<span style="mso-spacerun:yes">� </span>These exercises (and Excel) were developed after the book was published.<p></p></span></p> <p class="MsoListParagraphCxSpFirst" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.1.xls" target="_parent">Exercise 3.1</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.2.xls" target="_parent">Exercise 3.2 </a><span style="mso-spacerun:yes">��</span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.7.xls" target="_parent">Exercise 3.7</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.9_Revised.xls" target="_parent">Exercise 3.9 </a><span style="mso-spacerun:yes">���</span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.10.xls" target="_parent">Exercise 3.10</a><span style="mso-spacerun:yes">� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.11.xls" target="_parent">Exercise 3.11 </a><span style="mso-spacerun:yes">��</span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.12.xls" target="_parent">Exercise 3.12</a><span style="mso-spacerun:yes">� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.14.xls" target="_parent">Exercise 3.14</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.15.xls" target="_parent">Exercise 3.15</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.16.xls" target="_parent">Exercise 3.16</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.18.xls" target="_parent">Exercise 3.18</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.19.xls" target="_parent">Exercise 3.19</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.25.xls" target="_parent">Exercise 3.25</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpLast" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FExer3.28.xls" target="_parent">Exercise 3.28</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoNormal" style="margin-bottom:6.0pt;line-height:120%"><span style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'><p>�</p></span></p> <p class="MsoSubtitle" style="line-height:120%"><span style='font-size:18.0pt; mso-bidi-font-size:12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman"'>Other spreadsheets<p></p></span></p> <p class="MsoListParagraphCxSpFirst" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect1.3_Blast_Furnace.xls" target="_parent">Section 1.3.<span style="mso-spacerun:yes">� </span>Blast furnace example</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect1.3_Portfolio_Selection.xls" target="_parent">Section 1.3.<span style="mso-spacerun:yes">� </span>Portfolio selection example</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect1.4_Glass_Problem.xls" target="_parent">Section 1.4.<span style="mso-spacerun:yes">�� </span>Glass manufacturing example</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect2.3_Simple_Example.xls" target="_parent">Section 2.3.<span style="mso-spacerun:yes">�� </span>A simple example</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FFig2.4_Pivoting.xls" target="_parent">Figure 2.4.<span style="mso-spacerun:yes">�� </span>Pivoting</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FFig2.6_Pivoting.xls" target="_parent">Figure 2.6.<span style="mso-spacerun:yes">� </span>Pivoting.</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect3.1_Tableaus.xls" target="_parent">Section 3.1.<span style="mso-spacerun:yes">�� </span>Tableaus</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect3.6_Glasses.xls" target="_parent">Section 3.6.<span style="mso-spacerun:yes">�� </span>Glasses (again)</a><span style="mso-spacerun:yes">� </span><p></p></span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect3.6_Sensitivity.xls" target="_parent">Section 3.6.<span style="mso-spacerun:yes">�� </span>Sensitivity tableaus</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoListParagraphCxSpLast" style="margin-bottom:6.0pt;mso-add-space: auto;text-indent:-.25in;line-height:120%;mso-list:l2 level1 lfo5">&lt;![if !supportLists]&gt;<span style="font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:120%;font-family: Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol"><span style="mso-list:Ignore">�<span style='font:7.0pt "Times New Roman"'>������������ </span></span></span>&lt;![endif]&gt;<span style='font-size:11.0pt;mso-bidi-font-size: 12.0pt;line-height:120%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><a href="https://www.apklas.com?arsae=http%3A%2F%2Fweb.mit.edu%2F15.053%2Fwww%2FExcelExercises%2FSect4.2_Primal_Dual.xls" target="_parent">Section 4.2.<span style="mso-spacerun:yes">�� </span>Primal-Dual</a><span style="mso-spacerun:yes">�� </span><p></p></span></p> <p class="MsoNormal" style="margin-bottom:12.0pt"><span style='font-size:12.0pt; line-height:110%;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><p>�</p></span></p> </div> </body> </html>