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# Testing hypotheses of more population means

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(1) 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 Â½, 2 Â½, and 3 Â½ 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 Alternatives Number of Rolls Waste (inches)
1 Â½ in. 2 Â½ in. 3 Â½ in.
1 6 0 0 1
2 0 4 0 0
3 2 0 2 0
4 0 1 2 Â½
5 1 3 0 1
6 1 2 1 0
7 4 0 1 Â½

The minimum requirements for the three products are
Roll Width (inches) 1 Â½ 2 Â½ 3 Â½
Units 1000 2000 4000
a. If the company wants to minimize the number of 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)?
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)?
c. What are the differences in approaches (a) and (b) to this problem? In this case, which objective do you prefer? Explain. What types of situations would make the other objective more desirable?

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#### Solution Preview

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(1) 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 Â½, 2 Â½, and 3 Â½ 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 Alternatives Number of Rolls Waste (inches)
1 Â½ in. 2 Â½ in. 3 Â½ in.
1 6 0 0 1
2 0 4 0 0
3 2 0 2 0
4 0 1 2 Â½
5 1 3 0 1
6 1 2 1 0
7 4 0 1 Â½
The minimum requirements for the three products are
Roll Width (inches) 1 Â½ 2 Â½ 3 ...

#### Solution Summary

The solution contains detailed explanation of testing whether the population means are the same.

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