ARE155FA10MT1_va_KEY

ARE155FA10MT1_va_KEY - Name:_KEY_ Last 4 digits of your...

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Name:_KEY_________________ Last 4 digits of your Student ID Number:__________ Managerial Economics (ARE) 155 University of California, Davis, Fall 2010 Dr. John H. Constantine Midterm 1, Friday, October 15, 2010 80 TOTAL POINTS WARNINGS : (1) NO CALCULATORS ALLOWED! (2) All problems require that you show your work. If no work is shown, then no credit is given .
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1 Problem 1 (30 total points) : IMPORTANT NOTE: This problem requires numeric solutions for all parts—you must show all work. In addition, if asked, you are to provide a brief explanation for what your numeric solution means. You are given the following primal LP, where the x j are outputs, the c j are output prices and the constraints are input availabilities: max z = 10x 1 + 10x 2 + 10x 3 st 2x 1 + x 2 + 2x 3 50 x 1 + 2x 2 + 2x 3 150 x j 0 (j = 1,2,3) (a) Calculate (by hand) numeric values for all x j * and s i * . (20 points.) To do this problem, you need to solve the dual LP . The dual for this problem is: min TC = 50y 1 + 150y 2 st 2y 1 + y 2 10 y 1 + 2y 2 10 2y 1 + 2y 2 10 y i 0 (i = 1, 2, 3) The dual solution is solved (see the graph on the following page), and using the C-S conditions the primal solution is attained: y 1 * = 10 s 1 * = 0 y 2 * = 0 s 2 * 0 (s 2 * is potentially non-zero) y s1 * =10 x 1 * = 0 y s2 * = 0 x 2 * 0 (x 2 * is potentially non-zero) y s3 * = 10 x 3 * = 0 TC* = 500 We can rewrite the primal LP by eliminating all known zero values, thus worrying only about the potential non-zero values: max z = 10x 2 st x 2 = 50 x 2 + s 2 = 120 x 2 , s 2
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This note was uploaded on 11/09/2010 for the course ARE ARE155 taught by Professor Constantine,john during the Fall '10 term at UC Davis.

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ARE155FA10MT1_va_KEY - Name:_KEY_ Last 4 digits of your...

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