Chapter 13.9, Problem 16E

To determine

To calculate: The quantities of candles to be produced at each location so the profit is maximized wherein, the cost functions for producing $x_1$ candles at location 1 and $x_2$ candles at location 2 are as below:

$\begin{array}{c}{C}_1=0.02x_1{}^2+4x_1+500\\ C_2=0.05x_2{}^2+4x_2+275\end{array}$

The profit functions $P$ for producing $x_1$ candles at location 1 and $x_2$ candles at location 2.

$P=15\left(x_1+x_2\right)-C_1-C_2$