Par, Inc., is a small manufacturer of golf equipment whose management has decided to
move into the market for medium- and high-priced golf bags. Par, Inc.’s distributor is
enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc.,
produces over the next three months.
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:
1. Cutting and dyeing the material
2. Sewing
3. Finishing (inserting umbrella holder, club separators, etc.)
4. Inspection and packaging
The director of manufacturing analyzed each of the operations and concluded that if
the company produces a medium-priced standard model, each bag will require 7/10 hour in the
cutting and dyeing department, 1/2 hour in the sewing department, 1 hour in the finishing department, and 1/10 hour in the inspection and packaging department. The more expensive deluxe
model will require 1 hour for cutting and dyeing, 5/6 hour for sewing, 2/3 hour for finishing, and
¼ hour for inspection and packaging. This production information is summarized in Table 2.1.
Par, Inc.’s production is constrained by a limited number of hours available in each
department. After studying departmental workload projections, the director of manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for
finishing, and 135 hours for inspection and packaging will be available for the production
of golf bags during the next three months.
The accounting department analyzed the production data, assigned all relevant variable
costs, and arrived at prices for both bags that will result in a profit contribution1
of $10 for
every standard bag and $9 for every deluxe bag produced. Let us now develop a mathematical
model of the Par, Inc., problem that 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. Refer to the Par, Inc., problem described in
Section 2.1. Suppose that Par, Inc., management encounters the situations described
below. Assuming that Par, Inc., encounters each of these situations separately, what is
the optimal solution and the total profit contribution for each situation described?
a. The accounting department revises its estimate of the profit contribution for the
deluxe bag to $18 per bag.
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.)
c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A 1 9B is the appropriate objective function.)
