Final answer:
Cammy can model her profit using the equation P(x) = (40 + 10x) × ($7 - x), where x is the number of dollars she decreases the price. By finding the maximum of this profit function, she can determine the optimal number of cheeseburgers to sell to maximize profit.
Step-by-step explanation:
Cammy is trying to determine the optimal pricing and sales strategy for selling cheeseburgers. Initially, she can sell 40 burgers a day at a $7 profit each. She believes that for each dollar she reduces her price, she can sell 10 additional burgers. To model this situation, let x be the number of dollars by which Cammy decreases the price per burger, and let P(x) be her total profit. The equation will consider both the increasing number of sales with the decreasing price and the effect on profit. The profit function can be defined as:
P(x) = (Number of burgers sold) × (Profit per burger)P(x) = (40 + 10x) × ($7 - x)
To find the maximum profit, Cammy can use calculus to find the vertex of the parabola or complete the square, or she can use a table or graph to find the maximum value of P(x) given her constraints. The goal is to find the best number of burgers she can sell at the optimal price decrease to maximize her profit.