Solved: Maximum Profit A corporation manufactures candles at two locations. The cost of

Chapter 13, Problem 16

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Maximum Profit A corporation manufactures candles at two locations. The cost of producing \(x_{1}\) units at location 1 is

\(C_1=0.02x_1^{\ 2}+4x_1+500\)

and the cost of producing \(x_{2}\) units at location 2 is

\(C_2=0.05x_2^{\ 2}+4x_2+275\)

The candles sell for $15 per unit. Find the quantity that should be produced at each location to maximize the profit \(P=15\left(x_{1}+x_{2}\right)-C_{1}-C_{2}\).

Text Transcription:

x_1

C_1 = 0.02x_1 ^2 + 4x_1 + 500

C_2 = 0.05x_2 ^2 + 4x_2 + 275

P = 15(x_1 + x_2) - C_1 - C_2

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