EE
hw2IE5112

# H what is the shadow price for raw material i perform

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(h) What is the shadow price for raw material? (i) Perform sensitivity analysis on the raw material constraint. What is the range over which the shadow price for raw material is valid? (j) Perform sensitivity analysis on the coefficients in the objective function. Suppose that the com- pany is considering raising prices on the deluxe version of the product in order to increase profit. The profit for one unit of the deluxe product is currently 15. What is the upper limit on this coefficient for which the current optimal solution will remain unchanged?

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5. (20 pts) Consider the following linear programming problem. max Z = 4 x 1 + 2 x 2 subject to 2 x 1 16 (resource 1) x 1 + 3 x 2 12 (resource 2) x i 0 , i = 1 , 2 (a) Solve this problem graphically 5 10 5 10 x 2 x 1 (b) There is a shadow price associated with each resource. Which (if any) of the resources have a strictly positive shadow price? (c) The coefficient of x 1 in the objective function is currently equal to 4. Determine the allowable range for this coefficient, call it c 1 , over which the current solution remains optimal. Your answer will have the form l c 1 u , where l and u define the range. References [1] Paul Williams. Model Building in Mathematical Programming . John Wiley and Sons, fourth edition, 1999.
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