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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 4351(5)
= 440.
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 Spring '07
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