Linear Programming using MATLAB or LINDO

Product Mix Problem

Acme Industries produces four types of mens 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: 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.

Formulate the problem as a linear program with an objective function and all constraints (This means "What are the decision variables?" "What are the indices/sets?").

1. Determine the optimal solution for the linear program using MATLAB or LINDO.

2. What are the optimal numbers of ties of each type to maximize profit?

3. Include a copy of the code and output.

If you don't have access to MATLAB or LINDO, you CANNOT respond to this question.

Thanks!

Material Silk Polyester Cotton Cost per yard $20 $6 $9 Yards available er month 1,000 2,000 1,250 Type of Tie Silke s Poly = p $6.70 Product Information Selling Price per tie Monthly Minimum units 6,000 Monthly Maximum units 7,000 $3.55 10,000 14,000 Blend1s b Blend2-c $4.31 13,000 16,000 $4.81 6,000 8,500 Type of Tie Material Information in ards Silk PolyesterBlend 1 Blend 2 (50/50) (30/70) Silk Polyester Cotton 0.125 0 0 0 0.08 0 0 0.05 0.05 0 0.03 0.07 selling price type labor material profit per tie silk s poly p blend1 b blend2 c 6.7 3.55 4.31 4.81 0.75 0.75 0.75 0.75 2.5 0.48 0.75 0.81 3.45 2.32 2.81 3.25 Material Silk Polyester Cotton Cost per yard $20 $6 $9 Yards available er month 1,000 2,000 1,250 Type of Tie Silke s Poly = p $6.70 Product Information Selling Price per tie Monthly Minimum units 6,000 Monthly Maximum units 7,000 $3.55 10,000 14,000 Blend1s b Blend2-c $4.31 13,000 16,000 $4.81 6,000 8,500 Type of Tie Material Information in ards Silk PolyesterBlend 1 Blend 2 (50/50) (30/70) Silk Polyester Cotton 0.125 0 0 0 0.08 0 0 0.05 0.05 0 0.03 0.07 selling price type labor material profit per tie silk s poly p blend1 b blend2 c 6.7 3.55 4.31 4.81 0.75 0.75 0.75 0.75 2.5 0.48 0.75 0.81 3.45 2.32 2.81 3.25