hw11solutions - IEOR 162 Linear Programming Spring 2007...

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IEOR 162 Linear Programming Spring 2007 Homework 11 Solutions 6.8.5 (4 points) a. The company is maximizing revenue instead of profit because costs have already been paid in order to acquire raw material and labor. b. y 1 = 0 (more skilled labor is not useful), y 2 = 0 (more unskilled labor is not useful), y 3 = 15 (an additional unit of raw material is worth $15 to us), y 4 = - 5 (for each additional product 2 required, we lose $5). c. Revenue will be equal to the original revenue plus the change in raw material multiplied by its shadow price. Revenue is thus equal to 435+5(15) = 510. d. Since the shadow price of skilled labor is 0, if the current basis remains optimal, changing the amount of skilled labor available does not change the objective. It should be noted that if skilled labor is only 80 hours that the current basis is no longer feasible, so you would need to use the dual simplex method to obtain the new optimal solution. e. Assuming the current basis remains optimal, if 5 units of product 2 were required, then the new revenue would be equal to 435+2(-5) = 425. If only 2 units were required then revenue would be equal to 435-1(-5) = 440.
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hw11solutions - IEOR 162 Linear Programming Spring 2007...

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