Chapter 2.3, Problem 71E

Break-even analysis. Use the revenue function from Problem $69$ and the given cost function:

$\begin{array}{l}R\left(x\right)=x\left(75-3x\right)\text{ Revenue function}\\ C\left(x\right)=125+16xCost\text{function}\end{array}$

where $x$ is in millions of chips, and $R\left(x\right)$ and $C\left(x\right)$ are in millions of dollars. Both functions have domain $1\le x\le 20$.

(A) Sketch a graph of both functions in the same rectangular coordinate system.

(B) Find the break-even points to the nearest thousand chips.

(C) For what values of $x$ will a loss occur? A profit?