Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations: cutting and dyeing the material, sewing, finishing, and inspection and packaging. A mathematical model has been developed that shows the constraints of production, time, and cost. It can be used to determine the number of standard bags and the number of deluxe bags to produce in order to maximize total profit contribution.

LetS= number of standard bags.

LetD= number of deluxe bags.

Max10S+ 9Ds.t.7

10

S+ 1D630Cutting and Dyeing1

2

S+5

6

D600Sewing1S+2

3

D708Finishing1

10

S+1

4

D135Inspection and PackagingS,D0

Refer to the Par, Inc., problem described above and in Section 2.1. Suppose that Par, Inc., management encounters the following situations.

If each of these situations is encountered separately, what is the optimal solution and the total profit contribution?

(a)

The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.

The optimal solution occurs at(S,D) =540S+252D

with a profit of$7668.

(b)

A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.)

The optimal solution occurs at(S,D) =540S+252D

with a profit of$13068.

(c)

New sewing equipment is available that would increase the sewing operation capacity to625hours. (Assume that10A+ 9B

is the appropriate objective function.)

The optimal solution occurs at(S,D) =540S+252S

with a profit of$.