26 Wivco produces two products: 1 and 2. The relevant data are shown in Table 64. Each...

Question:

26 Wivco produces two products: 1 and 2. The relevant data are shown in Table 64. Each week, as many as 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 can be asked to work overtime and are paid $6 per hour for overtime work. Each week, 320 hours of machine time are available.

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; 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 material 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:

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to answer the following questions:
a If overtime were 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?
e If each worker were required (as part of the regular workweek) to work 45 hours per week, what would the company’s profits be?
f Explain why the shadow price of row (1) is 0.10.
(Hint: If the right-hand side of (1) were increased from 50 to 51, then in the absence of advertising for product 1, 51 units could now be sold each week.)
g Wivco is considering producing a new product (product 3). Each unit sells for $17 and requires 2 hours of labor, 1 unit of raw material, and 2 hours of machine time. Should Wivco produce any of product 3?
h If each unit of product 2 sold for $10, would the current basis remain optimal?