Chapter 6.3, Problem 15E

In Exercises 15-22, assume that relative maximum and minimum values are absolute maximum and minimum values.

Maximizing profit. Safe Shades produces two kinds of sunglasses; one kind sells for $17, and the other for $21.The total revenue in thousands of dollars from the sale of x thousand sunglasses at $17 each and y thousand at $21 each is given by

$R\left(x,y\right)=17x+21y.$

The company determines that the total cost, in thousands of dollars, of producing x thousand of the $17 sunglasses and y thousand of the $21 sunglasses is given by

$C\left(x,y\right)=4x^2-4xy+2y^2-11x+25y-3$

How many of each type of sunglasses must be produced and sold to maximize profit?