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$, find a daily revenue function, $R(x)$, which calculates the income for $x$ calculators sold.

   Answer (a):

   $R(x) = 90x$

2. Find the profit function, $P(x)$, which calculates the profit per day when x calculators are produced and each later sold for $\$90$.

   Hint (b):

   Profit is the difference between revenue and cost of product.

3. Find the daily production that will maximize the profit.

   Step (c):

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

4. What is the maximum daily profit?

   Step (d):

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