3. A global textile manufacturer produces two types of sweaters: embroidered swe
ID: 2527339 • Letter: 3
Question
3. A global textile manufacturer produces two types of sweaters: embroidered sweaters and graphic tee sweaters. Both sweaters are made of cotton. Due to their long and strong relationships over the years, the supplier of the cotton has decided to offer quantity discounts to the textile company. More specifically, the supplier will reduce the cost of the cotton by $0.01 for each 30 pounds of cotton the textile company buys. The original price of the cotton is $1.5 per pound. The textile company is allowed to purchase at most 300 pounds of cotton. The company processes every pound of cotton into a single embroidered sweater, which sells for $70 each, and into two graphic tee sweaters, which sells for $50 each. The embroidered sweaters cost the company additional $20 in labor and the graphic tee sweaters cost the company $10 in labor The company wants to keep its costs below $20,000. How many of embroidered sweaters and graphic tees sweaters should the company make to maximize its revenue?Explanation / Answer
Solution 1:
Let’s compute the contribution achieved by 1 pound of cotton:
1 pound of cotton produces 1 embroidered sweater and 2 graphic tee sweaters.
A single pound of cotton contribution statement will look like below:
Particulars
Total
1 Embroidered Sweater
2 graphic tee
Calculation for Graphic tee
Revenue
170
70
100
(50*2)
Less: Direct labor
30
20
10
($10 for 2 tee sweaters)
Revenue net of Labor
140
50
90
Less: Cost of material
1.499666667
Net Contribution
138.5003333
Since $0.01 will be saving for every purchase of 30 pounds, per pound saving in raw material will translate to $0.01 / 30 = $ 0.00033
A single pound of cotton would demand a cost of $30 + $1.49966= $31.50(rounded off). Since a company can spend maximum of $20,000, it will have to work on $20,000 / 31.5 = 635 pounds (rounded off).
From 635 pounds, company will sell 635 embroidered sweater and 1270 graphic tee sweaters (635*2)
For 635 pounds cotton, income statement will look like below:
Particulars
Total
635 Embroidered Sweater
1270 graphic tee
Calculation for Graphic tee
Revenue
107,950
44450
63500
(1270*50)
Less: Direct labor
19,050
12700
6350
(635*2*10)
Revenue net of Labor
88,900
31750
57150
Less: Cost of material
952
Net Contribution
87,948
Total Cost would be $19,050 + 952 = $20,002 (approx)
Particulars
Total
1 Embroidered Sweater
2 graphic tee
Calculation for Graphic tee
Revenue
170
70
100
(50*2)
Less: Direct labor
30
20
10
($10 for 2 tee sweaters)
Revenue net of Labor
140
50
90
Less: Cost of material
1.499666667
Net Contribution
138.5003333
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