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

Chapter 13, Problem 14

(choose chapter or problem)

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

$C_{1}=0.02 x_{1}^{2}+4 x_{1}+500$

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

\(C_{2}=0.05 x_{2}^{2}+4 x_{2}+275\).

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

x_2

C_2 = 0. 05x_{2}^{2} + 4x_2 + 275

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