IOE310_PS08_Solution

# IOE310_PS08_Solution - IOE 310 Problem Set 08 Solutions...

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IOE 310 - Problem Set 08 Solutions Problem 1 Section 6.5 Problem 2 (p.301) SKIP Assigned for PS09. :-) Problem 2 Section 6.5 Problem 3 (p.301) We are given the following LP: max z =4 x 1 x 2 +2 x 3 s.t x 1 + x 2 5 2 x 1 + x 2 7 2 x 2 + x 3 6 x 1 + x 3 x 1 0 x 2 , x 3 urs The dual of this problem is: min w =5 y 1 +7 y 2 +6 y 3 +4 y 4 s.t y 1 y 2 + y 4 4 y 1 + y 2 y 3 = 1 y 1 , y 2 0, y 3 0, y 4 urs

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IOE 310 – Problem Set 08 Page 2 of 5 Problem 3 Section 6.6 Problem 1 (p.304) The original LP and the solution to this are given on page 64 of the text. Looking at this we know already that we are only producing trucks in the optimal solution and that the constraint on the paint shop is binding (or otherwise is 100% utilized). Formulating the LP of this problem we get: min y 1 + y 2 s.t 1 / 40 y 1 +1 / 50 y 2 3 1 / 60 y 1 / 50 y 2 2 y 1 , y 2 0 Plugging this into Microsoft Excel or AMPL we would ±nd that y 1 = 120 and y 2 = 0 (units are hundreds of dollars). The economic interpretation of this dual is thus:
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## This note was uploaded on 12/20/2010 for the course IOE 310 taught by Professor Saigal during the Fall '08 term at University of Michigan.

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IOE310_PS08_Solution - IOE 310 Problem Set 08 Solutions...

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