Question

Paper trim problem: The Oblivion 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 1½, 2½, and 3½ 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 five cutting alternatives and the amount of waste generated by each are as follows:

Cutting Alternative

Number of Rolls 1 ½ in 2 ½ in 3 ½ in

Waste (inches)

1	6	0	0	1
2	0	1	2	.5
3	1	3	0	1
4	1	2	1	0
5	4	0	1	0.5

The minimum product requirements for the three products are as follows:

Roll Width (inches)	Units
1 ½	4000
2 ½	1500
3 ½	1000

With the goal of minimizing the number of units of the 10-inch rolls will be processed on each cutting alternative, find each of the following:
Total Number of 10-inch Rolls Processed =

Note: Value is between 1360 and 1390
Number of 1½ inch rolls produced =

Number of 2½ inch rolls produced =

Number of 3½ inch rolls produced =

Number of Rolls Cut Using Alternative 1 =

Number of Rolls Cut Using Alternative 4 =

Number of Rolls Cut Using Alternative 5 =

Answer 1

I have used excel to solver the problem -

Below is the screenshot of the LP table -

Below is the screenshot of the formula applied -

Below is the screenshot of the solver -

Below is the screenshot of the result -

Total Number of 10-inch Rolls Processed = 1375

Number of 1½ inch rolls produced = 4000

Number of 2½ inch rolls produced = 1500

Number of 3½ inch rolls produced = 1000

Number of Rolls Cut Using Alternative 1 = 375

Number of Rolls Cut Using Alternative 4 = 750

Number of Rolls Cut Using Alternative 5 = 250