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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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