Question

Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 150. Its cost (in dollars) for a run of x hockey jerseys is
C(x) = 1500 + 10x + 0.2x2 (0 ≤ x ≤ 150)
1. Gymnast Clothing sells the jerseys at $90 each. Find the revenue function.
2. Find the profit function.
3. How many should Gymnast Clothing manufacture to make a profit?

Answer 1

The Revenue function for the number of jerseys x sold is ; R(x) = 90x

The profit function from the sale of x jerseys is ; P(x) = - 0.2x² + 80x - 1500

The number of Jerseys to manufacture in other to make profit = 20

The revenue made is the total amount made from the sale of the hickey jerseys :

Sales price per jersey = $90

Hence, the revenue made, R(x) = 90x

The Cost function, C(x) = C(x) = 1500 + 10x + 0.2x²

Recall :

Profit = Revenue - Cost

Hence,

P(x) = R(x) - C(x)

P(x) = 90 - (0.2x² + 10x + 1500)

P(x) = 90 - 0.2x² - 10x - 1500

P(x) = - 0.2x² + 80x - 1500

To make profit, equate P(x) to 0 ;

0.2x² - 80x + 1500 = 0

Using a quadratic calculator :

x = 380.22 or x = 19.72

Hence, to make a profit, the number of jerseys that must be sold is 20.

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