* Please show how you formulated the problem as a linear program with an objective function and all constraints. Thank you!

2. Product Mix: (7 points) 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, 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. Yards available Material Cost per yard $20 $6 $9 r month 1,000 2,000 1,250 Polvester Cotton Type of Tie Silk-sPolyp $6.70 Product Information Selling Price per tie Monthly Minimum units 6,000 Monthly Maximum units 7,000 S3.55 10,000 14,000 Blend! = 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 30/70 50/50 0.125 Polvester 0.08 0.05 0.03 Cotton 0.05 0.07 selling material lling labor rice type profit per le 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 Formulate the problem as a linear program with an objective function and all constraints. Determine the optimal solution for the linear program using any software you want. What are the optimal numbers of ties of each type to maximize profit? Include a copy of the code and output