Wivco produces two products: 1 and 2. The relevant data are shown in Table 12. Each week, up to 400 units of raw material can be purchased at a cost of $ 1.50 per unit. The company employs four workers, who work 40 hours per week. (Their salaries are considered a fixed cost.) Workers are paid $6 per hour to work overtime. Each week, 320 hours of machine time are available. Product 1 Product 2
Selling price ($) 15 8
Labor required (hours)         0.75       0.50
Machine time required (hours)       1.5       0.80
Raw material required (units)   2 1

In the absence of advertising, 50 units of product 1 and 60 units of product 2 will be demanded each week. Advertising can be used to stimulate demand for each product. Each dollar spent on advertising product 1 increases its demand by 10 units, and each dollar spent for product 2 increases its demand by 15 units. At most $100 can be spent on advertising. Define

P1 = number of units of product 1 produced each week
P2 = number of units of product 2 produced each week
OT = number of hours of overtime labor used each week
RM = number of units of raw materials purchased each week
A1 = dollars spent each week on advertising product 1
A2 = dollars spent each week on advertising product 2

Then Wivco should solve the following LP:

maxz=15Pl+8P2−6(OT)−1.5RM−Al−A2
s. t.P1−10A1≤50(1)
P2−15A2≤60(2)
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0.75P1+0.5P2
2P1+P2
RM
A1+A2
1.5P1+0.8P2
All variables non-negative
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amp;≤160+(OT)(3)
mp;≤RM(4)
amp;≤400(5)
amp;≤100(6)
amp;≤320(7)

Required:
a. If overtime cost only $4 per hour, would Wivco use it?
b. If each unit of product 1 sold for $15.50, would the current basis remain optimal? What would be the new optimal solution?
c. What is the most that Wivco should be willing to pay for another unit of raw material?
d. How much would Wivco be willing to pay for another hour of machine time?
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