A company is planning to manufacture and market a new four-slice toaster. For this toaster, the research department's estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department's estimates are fixed weekly costs of $5000 and variable costs of $5 per toaster.
(a) Assume that the relationahip between price p and demand x is linear. Use the research department's estimates to express p as a function of x, and find the domain of this function.
(b) Find the revenue function R(x) from the sale of x pairs of running shoes, and state its domain.
(c) Evaluate the marginal revenue at x=325 and x=425 and interpret the results.