Chapter 2.3, Problem 4MP

Use the profit equation from matched problem $3$ :

$\begin{array}{c}P\left(x\right)=R\left(x\right)-C\left(x\right)\\ =-5x^2+75.1x-156\text{ Profit function}\\ \text{domain}:1\le x\le 15\end{array}$

(a) Sketch a graph of the profit function in a rectangular coordinate system.

(b) Break even points occur when $P\left(x\right)=0$ find the break-even points algebraically to the nearest thousand cameras

(c) Plot the profit function in an appropriate viewing window.

(d) Find the break-even point graphically to the nearest thousand cameras.

(e) A loss occurs if $P\left(x\right)<0$, and a profit occurs if $P\left(x\right)>0$ for what values of $x$ (to the nearest thousand cameras) will a loss occur? A profit?