Chapter 4, Problem 31LOR

For Questions 28–37, refer to the following: From years of experience, a bagel shop has determined that at a price of , they will sell $\mathrm{x\; <mo>\; =\; <mn>\; 450\; </mn>\; </mo>}$ bagels each week. If they lower the price to , they will sell $\mathrm{x\; <mo>\; =\; <mn>\; 550\; </mn>\; </mo>}$ bagels each week.

The profit made by the sale of these bagels is found by subtracting the costs from the revenue: . Find an equation that represents profit by substituting your expressions for R and C into the profit formula. Simplify your answer.