Acme Industries produces four types of men’s ties using three types of material. Your job is to determine how many of each type of tie to make each month. The goal is to maximize profit, where profit per tie = selling price - labor cost – material cost. Labor cost is $0.75 per tie for all four types of ties. The material requirements and costs are given below. Material Cost per yard Yards available
per month
Silk $20 1,000
Polyester $6 2,000
Cotton $9 1,250
Type of Tie
Product Information Silk Polyester Blend 1 Blend 2
Selling Price per tie $6.70 $3.55 $4.31 $4.81
Monthly Minimum units 6,000 10,000 13,000 6,000
Monthly Maximum units 7,000 14,000 16,000 8,500
Type of Tie
Material Information in yards Silk Polyester Blend 1 Blend 2
(50/50) (30/70)
Silk 0.125 0 0 0
Polyester 0 0.08 0.05 0.03
Cotton 0 0 0.05 0.07
a) Formulate the problem as a linear program with an objective function and all constraints.
b) Determine the optimal solution for the linear program using any software you want. Include a copy of the code and output.
c) What are the optimal numbers of ties of each type to maximize profit.