Chapter 4.2, Problem 79E

Profit The demand equation for a microwave oven is given by $p=140-0.0001x$, where p is the unit price (in dollars) of the microwave oven and $x$ is the number of units sold. The cost equation for the microwave oven is $C=80x+150,000$, where $C$ is the total cost (in dollars) and $x$ is the number of units produced. The total profit $P$ obtained by producing and selling $x$ units is modeled by $P=xp-C$.

(a) Find the profit function $P$ in terms of $x$.

(b) Find the profit when $250,000$ units are sold.

(c) Find the unit price when $250,000$ units are sold.

(d) Find (if possible) the unit price that will yield a profit of 10 million dollars. If not possible, explain why.