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A sporting goods manufacturer produces regulation soccer balls at two plants. The costs of producing x1x_1 units at location 1 and x2x_2 units at location 2 are given by C1(x1)=0.02x12+4x1+500C_1\left(x_1\right)=0.02 x_1^2+4 x_1+500 and

C2(x2)=0.05x22+4x2+275C_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(x1,x2)=50(x1+x2)C1(x1)C2(x2).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).


Answered 1 year ago
Answered 1 year ago

From the given functions PP, C1C_1 and C2C_2, we have

P(300,200)=45×(300+200)C1(300)C2(200)=180001800170020001775=15925.\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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