Problem Men’s Wear, Inc., a nationally known manufacturer of menswear, produces
ID: 2419004 • Letter: P
Question
Problem
Men’s Wear, Inc., a nationally known manufacturer of menswear, 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 first table below illustrates the cost and availability (per monthly production planning period) of the three materials used in the production process.
The company has fixed contracts with several major department store chains to supply ties each month. The contracts require that Men’s Wear supply a minimum quantity of each tie but allow for a larger demand if Men’s Wear chooses to meet that demand. (Most of the ties are not shipped with the name Men’s Wear on their label, incidentally, but with “private stock” labels supplied by the stores.) The second table below summarizes the contract demand for each of the four styles of ties, the selling price per tie, and the fabric requirements of each variety. The production process for all ties is almost fully automated, and Men’s Wear uses a standard labor cost of $0.75 per tie for any variety.
Men’s Wear must decide on a policy for product mix in order to maximize its monthly profit. What is the optimal monthly profit for Men’s Wear and how many ties of each type should they produce per month?
Material
Cost Per Yard
Material Available
Per Month (yards)
Silk
$20
1,000
Polyester
$6
2,000
Cotton
$9
1,250
Variety of Tie
Selling
Price Per Tie
Monthly
Contract
Minimum
Monthly
Demand
Total Material
Required Per
Tie (yards)
Material
Requirements
All silk
$6.70
6,000
7,000
0.125
100% silk
All polyester
$3.55
10,000
14,000
0.08
100% polyester
Poly-cotton blend 1
$4.31
13,000
16,000
0.10
50% polyester/50% cotton
Poly-cotton blend 2
$4.81
6,000
8,500
0.10
30% polyester/70% cotton
Develop answers to each of the questions below related to the procedure “Ten Steps to Solve Decision Analysis Problems”. Feel free to add more space as needed to respond to each of the ten questions.
Material
Cost Per Yard
Material Available
Per Month (yards)
Silk
$20
1,000
Polyester
$6
2,000
Cotton
$9
1,250
Explanation / Answer
NUMBER OF TIES PRODUCED:
Poly-cotton
blend 2
Poly = 255 yards
Cotton = 595 yards
Poly-cotton
blend 1
Poly = 655 yards
cotton = 655 yards
the optimal monthly profit for Men’s Wear = Total contribution - total labor costs =
(7000 * 4.2 + 8500 * 4 + 13100 * 3.56 + 13625 * 3.07) - 42225 * 0.75= 151864.75 - 31668.75 = $120196
Number of ties of each type should they produce per month = (SILK) 7000 + (POLY- COTTON BLEND-2) 8500 + (POLY- COTTON BLEND-1) 13100 + (ALL POLY) 13625 = 42225 numbers
Variety of Tie Contribution (net of material) Number of ties made material used Material un-used SILK 6.7 - 2.5=4.2 7000 @0.125 = 875 yards silk =125 yardsPoly-cotton
blend 2
4.81 - 0.81=4 8500Poly = 255 yards
Cotton = 595 yards
Poly-cotton
blend 1
4.31 - 0.75=3.56 13100Poly = 655 yards
cotton = 655 yards
All Poly 3.55 - 0.48 = 3.07 13625 Poly = 910 yards TOTAL 42225Related Questions
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