Home > APCALC > Chapter 6 > Lesson 6.3.2 > Problem6-97

6-97.

A calculator company found that the cost of producing $x$ graphing calculators per day is $C(x) = 5x + e^{0.02x}$. (This ignores the original research and development cost, which is quite large.)

1. If each calculator is priced at $90$, write an equation for the daily revenue, $R$, which calculates the income per day for $x$ calculators sold.

$R(x) = 90x$

2. Write an equation for the profit, $P$, which calculates the profit per day when $x$ calculators are produced and each later sold for $90$.

Profit is the difference between revenue and cost of product.

3. How many calculators should the company produce each day to maximize the profit?

Optimize your profit function. You are looking for an $x$-value.

4. What is the maximum daily profit?

Find the $P\left(x\right)$ value that corresponds to your answer in part (c).