STAR Co. providespaper to smaller companies whose volumes are not large enough towarrant dealing directly with the paper mill. STAR receives100-feet-wide paper rolls from the mill and cuts the rolls intosmaller rolls of widths 12, 15, and 30 feet. The demands for thesewidths vary from week to week. The following cutting patterns havebeen established:

	Numberof:
Pattern	12ft.	15ft.	30ft.	Trim Loss
1	5	0	1	10 ft.
2	0	0	3	10 ft.
3	3	0	2	4 ft.
4	3	2	1	4 ft.
5	7	1	0	1 ft.

Trim loss is theleftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) +2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss).Orders in hand for the coming week are 5,670 12-foot rolls, 1,68015-foot rolls, and 3,350 30-foot rolls. Any of the three types ofrolls produced in excess of the orders in hand will be sold on theopen market at the selling price. No inventory is held.

Optimal Solution:

(a)	Formulate an integer programmingmodel that will determine how many 100-foot rolls to cut into eachof the five patterns in order to minimize trim loss. If your answeris zero enter “0” and if the constant is \"1\" it must be entered inthe box.
	Min x1 + x2 + x3 + x4 + x5 s.t. x1 + x2 + x3 + x4 + x5 - Select your answer -≤≥=Item11 12-foot rolls x1 + x2 + x3 + x4 + x5 - Select your answer -≤≥=Item18 15-foot rolls x1 + x2 + x3 + x4 + x5 - Select your answer -≤≥=Item25 30-foot rolls x1,x2, x3,x4, x5 are integers
(b)	Solve the model formulated in parta. What is the minimal amount of trim loss?
	Trim Loss:  feet
	How many of each pattern should beused and how many of each type of roll will be sold on the openmarket? If your answer is zero enter “0”.
	Pattern Number RollsUsed 1 2 3 4 5