Chapter 8.3, Problem 69E

$P(x)=R(x)-C(x),$

where $R$ and $C$ are the revenue and cost functions, respectively. Use these function to solve Exercises 69–70.

Hunky Beef, a local sandwich store, has a fixed weekly cost of $525.00, and variable costs for making a roast beef sandwich are $0.55.

a. Let $x$ represent the number of roast beef sandwiches made and each week. Write the weekly cost function, $C$, for Hunky Beef.

b. The function $R(x)=-0.001x^2+3x$ describes the money that Hunky Beef takes in each week from the sale of $x$ roast beef sandwiches. Use this revenue function and the cost function from part (a) to write the store’s weekly profit function, $P$.

c. Use the store’s profit function to determine the number of roast beef sandwiches it should make and sell each week to maximize profit. What is the maximum weekly profit?