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Question

A sporting goods manufacturer produces regulation soccer balls at two plants. The costs of producing $x_1$ units at location 1 and $x_2$ units at location 2 are given by $C_1\left(x_1\right)=0.02 x_1^2+4 x_1+500$ and

$C_2\left(x_2\right)=0.05 x_2^2+4 x_2+275$

respectively. If the product sells for $50 per unit, then the profit function for the product is given by

$P\left(x_1, x_2\right)=50\left(x_1+x_2\right)-C_1\left(x_1\right)-C_2\left(x_2\right) .$

Find P(300,200).

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

From the given functions $P$, $C_1$ and $C_2$, we have

$\begin{align*} P(300,200)=& 45\times(300+200) -C_1(300) - C_2(200)\\ & =18000 - 1800 -1700 -2000 -1775\\ & = 15925. \end{align*}$

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