Question: Wivco produces product 1 and product 2 by processing raw material. Up to 90 lb of raw material may be purchased at a cost o f $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 = number of pounds of raw material processed

P1 = number of pounds of raw material used to produce product 1

P2 = number of pounds of raw material used to produce product 2

To maximize profit, Wivco should solve the following LP:

Max 13 P1+13.2P2- 10 RM

s.t. P1+ P2 -RM \(\le \) 0

2 P1+ 3P2 \(\le \) 200

RM \(\le \) 90

0.33 P2 \(\le \) 40

P1, P2, RM \(\ge \) 0

Solve this LP, and use the output to answer the following questions:

1. If only 87 lb of raw material could be purchased, what would Wivco ^' s profit be?
2. If product 2 sold for $39.50/lb, what would be the new optimal solution?
3. What is the most that Wivco should be willing to pay for another pound of raw material?
4. What is the most that Wivco should be willing to pay for another hour of labor?
5. 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?

Please enter the answer to part a - what is the objective value that results?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document