8 Wivco produces product 1 and product 2 by processing raw material. As much as 90 lb of raw material may be purchased at a cost of $10/lb. One pound of raw material can be used to produce either 1 lb of product 1 or 0.33 lb of product 2. Using a pound of raw material to produce a pound of product 1 requires 2 hours of labor or 3 hours to produce 0.33 lb of product 2. A total of 200 hours of labor are available, and at most 40 pounds of product 2 can be sold. Product 1 sells for $13/lb, and product 2 sells for $40/lb. Let RM = pounds of raw material processed P1= pounds of raw material used to produce product 1 P2 = pounds of raw material used to produce product 2 To maximize profit, Wivco should solve the following LP:

Use the LINDO output in Figure 12 to answer the following questions:
a If only 87 lb of raw material could be purchased, what would be Wivco’s profits?

b If product 2 sold for $39.50/lb, what would be the new optimal solution?
c What is the most that Wivco should pay for another pound of raw material?
d What is the most that Wivco should pay for another hour of labor?
e Suppose that 1 lb of raw material could also be used to produce 0.8 lb of product 3, which sells for $24/lb.
Processing 1 lb of raw material into 0.8 lb of product 3 requires 7 hours of labor. Should Wivco produce any of product 3?

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= max z 13P1 + 40(0.33)P210RM s.t. RMP1 P2 2P1 + 3P2200 RM 90 0.33P2 = 40 P1, P2, RM 0