A corporation manufactures candles at two locations. The cost of producing x 1 u

Question

A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is

and the cost of producing x2 units at location 2 is

The candles sell for $13 per unit. Find the quantity that should be produced at each location to maximize the profit

A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is C1 = 0.02x12 + 4x1 + 530 and the cost of producing x2 units at location 2 is C2 = 0.05x22 + 4x2 + 250 The candles sell for $13 per unit. Find the quantity that should be produced at each location to maximize the profit

Explanation / Answer

Profit = 13 x1 - .02 x1^2 - 4 x1 -530

D Profit/dx1 = 13 - .04 x1 -4 = 0

x1 = 9 / .04 = 225

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Profit = 13 x2 - .05 x2^2 - 4 x2 - 250

Taking the derivative again and setting = zero for a max

x2 = 9 / .05 = 180

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