Question: A company manufactures three types of golf bags: Standard (S), Deluxe (D), and Lightweight (L). The production of each type of bag involves four different departments: Cutting and dyeing, Sewing, Finishing, Inspection and packaging. The number of manhours required by each department to produce one unit of each of S, D and L, and the total number of manhours available in each department are summarized in table 1 below. The profit contribution of each unit of S, D and L is shown in table 2.

To find the production quantity of each type of bags that would maximize the profit, the production manager prepares a Linear Programming (LP) model that represents the above data. The model formulation is as follows:

S, D, L >= 0

The model is solved using the “Solver” tool in Excel and the reports are shown in Exhibit 1. Based on the reports of Model 1 in this exhibit, answer the following questions.

a. What are the optimal production quantities? What is the optimal profit?

b. What is the amount of unused manhours in the 4 departments?

c. What should be the profit contribution per unit of D that makes it part of the product mix?

d. If the production cost of L increases by $ 1 per unit, would it still be in our optimal solution?

e. If 10 skilled employees joined the finishing department, what change will they cause on the daily profit?

The management decided that the quantity of Deluxe bags produced daily should be at least 30 % of the quantity of produced Standard bags. The production manager modifies his LP model to incorporate this additional requirement and the generated reports are presented in exhibit 1, under “model 2” heading.

f. What is the formulation of this additional constraint?

g. The marketing manager asked for 5 units to be used for promotional purpose. So, the production manager decides to produce a quantity of D that is equal to 30% of the quantity of S, to satisfy the daily demand, plus 5 more units for the promotion. How does this change the daily profit?