Midterm Practice Exam_sol - 1(25 points Consider the...

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1. (25 points) Consider the following linear programming problem: maxz= 3zi + 2X2 + 5X3 + X3 < 5 X2 + x 3 ç 6 x1 + x 2 + x 3 < 15 xO X2O X3>O (a) (3 points) Write out this LP in standard form and explain why the Simplex Algorithm starts with this form. 3c-+ 2X f 3 s 2 X2 = /1 7> (b) (5 points) Write out the matrix A and the vectors x, b and c so that the above standard form can be written in the matrix form: mazz= cTx Ax =b x>O ° 10 Oj L’ c 2
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IOE 310 Winter 2009 Midterm Exam February 18, 2009 Name: Instructions This is a closed book, closed notes exam. You may use one double-sided 8 × 11 inch note sheet and no calculators during the exam. Note that not all problems carry the same weight. Do the problems that you are most com- fortable with first and then move to others. There are 3 problems in the exam and 8 pages (including this one). You can use the back of each sheet for rough calculations. Please write your solutions to each problem in the space provided. Show all work and write legibly. Your grade will depend in part on the completeness and clarity of your answers.
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