Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is: C (x) = 2950 + 6x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $130 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?

Question

Mathematics

Phoenix Curtis

13 September, 18:32

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is: C (x) = 2950 + 6x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $130 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?

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Harper Reilly · Answer 1

Revenue, R = 130x

Profit, P = Revenue - Cost

P = R - C

P = 130x - 2950 + 6x + 0.1x^2

At P = 0

0 = - 2950 + 136x + 0.1x^2

X = 21.355, - 1381.355

Therefore, manufacture greater than 21.355 items to make profit.