Question: Question 4

The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1 ½, 2 ½, and 3 ½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The seven cutting alternatives and the amount of waste generated by each are as follows:

Cutting Number of Rolls Waste

Alternative 1½ in. 2½ in. 3½ in. (inches)

1 6 0 0 1

2 0 4 0 0

3 2 0 2 0

4 0 1 2 ½

5 1 3 0 1

6 1 2 1 0

7 4 0 1 ½

The minimum production requirements call for 1200 feet of 1½ in. paper, 3000 feet of 2½ in. rolls, and 6000 feet of 3½ in. rolls.

a) If the company wants to minimize the number of units of the 10-inch rolls that must be manufactured, how many 10-inch rolls will be processed on each cutting alternative? How many rolls are required, and what is the total waste (inches)? Assume that fractional rolls can be cut in this problem.

b) If the company wants to minimize the waste generated, how many 10-inch units will be processed on each cutting alternative? How many rolls are required, and what is the total waste (inches)? Comment on the comparison of the solutions of a) and b).

Hint: Think carefully about how you define the decision variables. It might help to think about the kind of instruction that you would have to give to the person in charge on the shop floor.