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# old-final - AGEC 7100 Old final Exam Name 1 Maximize Profit...

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AGEC 7100 Old final Exam Name ____________________________ 1. Maximize Profit = 5X1 + 3X2 + 4 X3 + 2X4 subject to: 2X1 + X2 + 3X3 + X4 10 3X1 + X2 + X3 15 X4 2 a) Set up the simplex tableau for this problem, including all required slack variables. (The space below may be larger than the space required.) b) What is the greatest number of decision variables (X variables) that can be basic? How do you know? 2. Look at the tableau below for a minimization problem. Cost X1 X2 X3 S1 S2 M1 M2 RHS obj 1 120.75 0 172.25 -100 24.75 0 -124.75 1628.75 r1 0 1.25 0 1.75 -1 0.25 1 -0.25 16.25 r2 0 0.75 1 0.25 0 -0.25 0 0.25 3.75 a) Is this solution optimal? How do you know? b) Read the current solution from the tableau (decision variables and cost) c) Circle the pivot element.

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3. Look at the tableau below, for a maximization problem. Prof x1 x2 x3 s1 s2 s3 rhs obj 1 1.5 0 0.25 0 2.25 0 40.5 r 1 00 . 5 1 - 0 . 501 r2 0 0.5 1 0 0 4.5 r3 0 -0.5 0 -0.25 0 1 2.5 1 a) Is this solution optimal? How do you know? b) Read the current solution (decision variables and costs) from the table. c) Now give the shadow prices (duals) on the two constraints.
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old-final - AGEC 7100 Old final Exam Name 1 Maximize Profit...

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