A steel mill produces sheets of steel in 3 sizes. These sizes are 100, 80 and 55 inches. Unfortunately,
demand is in 3 other sizes; 45,30 and 18 inches.How should the mill cut the sheets to minimize waste?
Possible combinations
		45" sheet	30" sheet	18" sheet	Waste (inches)	Number of sheets	Total Waste
1	100" sheet	2	0	0	10	1	10
2		1	1	1	7	1	7
3		1	0	3	1	1	1
4		0	3	0	10	1	10
5		0	2	2	4	1	4
6		0	1	3	16	1	16
7		0	0	5	10	1	10
8	80" sheet	1	1	0	5	1	5
9		1	0	1	17	1	17
10		0	2	1	2	1	2
11		0	1	2	14	1	14
12		0	0	4	8	1	8
13	55" sheet	1	0	0	10	1	10
14		0	1	1	7	1	7
15		0	0	3	1	1	1
	Totals	7	12	26		Total	122
	Demand	150	200	175
Problem
A steel mill produces sheets of steel in three different sizes. Demand, however, is in 3 other, smaller, sizes.
How should the company cut the sheets of steel in order to minimize waste?
Solution
1) There are only a limited number of ways to cut the sheets. The variables are the number of times we have
to cut a sheet in a certain way. In worksheet Cutstock these are defined as Sheets_used.
2) The constraints are simple and straightforward.
	Sheets_made = Demand
	Sheets_used >= 0 via the Assume Non-Negative option
	Sheets_used = integer
3) The objective is to minimize waste. This is defined on the worksheet as Total_waste.
Remarks
In some situations it may seem rather difficult to write out all the possibilities for cutting stock as is done in
this model. There is a technique that lets the computer do this, called column generation. It is beyond the
scope of this example to fully discuss this technique.