A small tailors' company wants to use at least 130 yards of fabric to sew evening skirts and dresses. A dress requires 4 yards of fabric and the production of a skirt will need 3 yards. Research shows that they will be able to sell at most three times as many skirts as dresses. A dress will take 10 hours to produce and a skirt will take 1 hour. They can assign to this work no more than 286 hours. Each dress will sell for $540, and each skirt will sell for $180. How many skirts should they sew to maximize the profit?

Question

Mathematics

Jacoby Huynh

10 October, 07:12

A small tailors' company wants to use at least 130 yards of fabric to sew evening skirts and dresses. A dress requires 4 yards of fabric and the production of a skirt will need 3 yards. Research shows that they will be able to sell at most three times as many skirts as dresses. A dress will take 10 hours to produce and a skirt will take 1 hour. They can assign to this work no more than 286 hours. Each dress will sell for $540, and each skirt will sell for $180. How many skirts should they sew to maximize the profit?

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Answers (1)

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Jenny Levine · Answer 1

Answer: 66 skirts

Step-by-step explanation:

Since research shows that they will be able to sell at most three times as many skirts as dresses, and a dress will take 10 hours to produce and a skirt will take 1 hour,

Let the time of production be in 3:1

For the production of the skirts and the dress.

If 3 hours are used to produce 3 skirts, then 10 hours will be used for 1 dress.

3 + 10 = 13

286/13 = 22

That is 22 dresses will be produced and 22 * 3 = 66 skirts will be produced.

Therefore, they should sew 66 skirts in order to maximise the profit.