QuestionGymnast Clothing's cost for $x$ pairs of cleats is $C(x)=3,250+8x+0.1x^{2}$. Selling price is \$130 per pair. Find revenue and profit functions. How many pairs for profit?

Studdy Solution
Since the number of pairs of cleats cannot exceed500, the value of $x_{2}$ is not feasible. Therefore, Gymnast Clothing should manufacture at least28 pairs of cleats (rounding up to the nearest whole number) to make a profit.
So, the revenue function is $R(x) =130x$, the profit function is $(x) = -0.x^{2} +122x -3250$, and Gymnast Clothing should manufacture at least28 pairs of cleats to make a profit.