Question

STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mil. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft . 15ft. 30ft. Trim Loss 1 5 0 1 10ft. 10 ft. 3 4 1 1 7 ft. 4 3 0 2 4 ft. Ift. 2 0 Trim loss is the leftover 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, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held.

****Solve the model formulated in part a. What is the minimal amount of trim loss?****
	Trim Loss: ____ feet

Answer 1

Part A.

Decision variables

Let x1, x2, x3, x4, x5 be the no. Of 100 feet rolls used in pattern 1, 2,3,4,5 respectively.

Objective

Minimise Z = 10*x1+ 10*x2+4*x3+ 7*x4+ 1*x5

Constraints

5*x1+ 0*x2+8*x3+ 4*x4+ 2*x5 >= 5670

0*x1+ 0*x2+0*x3+ 3*x4+ 1*x5 >= 1680

1*x1+ 3*x2+0*x3+ 0*x4+ 2*x5 >= 3350

x1, x2, x3, x4, x5 >= 0

SFS14 1 Decision Variables 2 x1 3 x2 4 X3 5 X4 6 x5 Set Objective: To: O Max By Changing Variable Cells: O Yalue ot: 282.5 SBS2-SBS6 1680 Subject to the Constraints: SBS14:SBS16SDS14:SDS16 Add Change Delete 9Objective 10 Minimize 2810 -10 B2+10 B3+4 B4+7 B5+1 B6 12 13 constraints 14 15 16 17 Column B Formula Reset All 5620 1680 > 3360 5620 1680 3350 Load/save 3"B5-B6 B2+3 B3+2 B6 Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options 19 Solving Method

Part B

Minimum trim loss = 2810

No. of roll used:

Pattern 1 = 0

Pattern 2 = 0

Pattern 3 = 282.5

Pattern 4 = 0

Pattern 5 = 1680