Fifth Avenue Industries, a nationally known manufacturer of men’s wears, produce
ID: 453276 • Letter: F
Question
Fifth Avenue Industries, a nationally known manufacturer of men’s wears, produces four varieties of ties. One is an expensive all silk tie, one is an all-polyester tie, and two are blends of polyester and cotton. The following table illustrates the cost and availability (per monthly production planning period) of the three materials used in the production process:
Material
Cost per yard ($)
Material available per month (yards)
Silk
24
1,200
Polyester
6
3,000
Cotton
9
1,600
The firm has fixed contracts with several major department store chains to supply ties. The contracts require that Fifth Avenue Industries supply a minimum quantity of each tie, but allow for a larger demand if Fifth Avenue chooses to meet that demand. Following table summarizes the contract demand for each of the four styles of ties, selling price per tie, and the fabric requirements of each variety.
Variety of Tie
Selling Price per tie
($)
Monthly contract
minimum
Monthly Demand
Material required per (Yards)
tie
Material
Requirements
All Silk
19.24
5,000
7,000
0.125
100% silk
All
Polyester
8.70
10,000
14,000
0.08
100% polyester
Ploycotton Blend I
9.52
13,000
16,000
0.10
50% Poly &
50% cotton
Ploycotton Blend II
10.64
5,000
8,500
0.11
60% Silk &
40% cotton
Required:
Fifth Avenue’s goal is to maximize profit. Formulate the problem. Use Excel Sover to determine the optimal solution.
Material
Cost per yard ($)
Material available per month (yards)
Silk
24
1,200
Polyester
6
3,000
Cotton
9
1,600
Explanation / Answer
There are four types of ties, that the firm is interested to produce and sell to earn maximum profits.
Therefore , Decision variables are defined as the number of ties of each variety to be produced and sell as per the conditions and or constraints given. Let us denote number of silk ties as S, number of all polyester as P and other two Blend I as B and for Blend II as C. The given information and the solution (using excel solver) is represented in the excel sheet as follows: Optimal solution represents 5112 number of silk ties and the other three varieties matching with the maximum demands of 14,000, 16,000 and 8,500 respectively and maximum profit is $412,028.9.
Decision Variables S P B C Values 5112 14000 16000 8500 Price per tie 19.24 8.7 9.52 10.64 462914.9 Constraints SumProd. Price/yard Available Silk Material 0.125 0 0 0.066 1200 24 1200 Polyester Material 0 0.08 0.05 0 1920 6 3000 Cotton Material 0 0 0.05 0.044 1174 9 1600 Cost per tie 3 0.48 0.75 1.98 50886 Minimum contract 5000 10000 13000 5000 Demand 7000 14000 16000 8500 Objective function-Maximum Profit = 412028.9Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.