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) = 3000 + 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?
Revenue = 130x
Correct: Your answer is correct.
Profit = −0.1x2+124x−3000
Correct: Your answer is correct.
At least_____pairs ?
how do you find pairs
To find the number of pairs, you need to solve for x in the given equation. In this case, the equation is C(x) = 3000 + 6x + 0.1x^2, where C(x) represents the cost.
To find the number of pairs Gymnast Clothing should manufacture to make a profit, you need to determine the value of x when the profit function is positive. The profit function is given by Profit = -0.1x^2 + 124x - 3000.
To solve for the number of pairs that would result in a positive profit, set the profit function greater than zero:
-0.1x^2 + 124x - 3000 > 0
Now, you can solve for x using the quadratic formula or factoring. Either way, you need to find the values of x when the equation is true.
By solving this equation, you will find the minimum number of pairs Gymnast Clothing should manufacture to make a profit.