Question 2: (One-dimensional cutting stock problem) Assume a large number of cardboard sheets with 23 inch width is available. From these 23 sheets, we need to cut sheets with width 6, 7, and 8 in only one direction. The demand for sheets with width 6, 7, and 8 is 3000, 1000, and 2000, respectively. We would like to minimize the wastage, while satisfying the demand.

Hints:

	Pattern 1	Pattern 2	Pattern 3	Pattern 4	Pattern 5	Pattern 6	Pattern 7	Pattern 8	Demand
6	0	2	2	1	1	1	0	0	3000
7	3	1	0	1	2	0	2	1	1000
8	0	0	1	1	0	2	1	2	2000
Waste	2	4	3	2	3	1	1	0

Formulate the optimization model for question 2: provide a list of decision variables (1 points), objective function (1 points), and constraints (3 points), and identify the optimal solution by Excel Solver (5 points).