Chapter 2.3, Problem 3MP

The financial department in example $3$, using statistical and analytical techniques (see Matched Problem $7$ in Section $2.1$ ), arrived at the cost function.

$c\left(x\right)=156+19.7x$ Cost function

Where $C\left(x\right)$ is the cost for manufacturing and selling $x$ million cameras.

(a) Using the revenue function from example $3$ and the preceding cost function write an equation for the profit function

(b) Find the value of $x$ to the nearest thousand cameras that will generate the maximum profit. What is the maximum profit to the nearest thousand dollars? Solve the problem algebraically by completing the square

(c) What is the wholesale price per camera that generates the maximum profit?

(d) Graph the profit function using an appropriate viewing window.

(e) Find the output to the nearest thousand cameras that will generate the maximum profit. What is the maximum profit to the nearest thousand dollars? Solve the problem graphically using the maximum command.