The company in Problem 39 is also planning to manufacture and market a 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 $5,000 and variable costs of $5 per toaster.
(A) Assume that the relationship 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 in terms of x and state its domain.
(C) Assume that the cost function is linear. Use the financial department's estimates to express the cost function in terms of x.
(D) Graph the cost function and revenue function on the same coordinate system for 0 ≤ x ≤ 800. Find the break-even points and indicate regions of loss and profit.
(E) Find the profit function in terms of x.
(F) Evaluate the marginal profit at x = 325 and x = 425 and interpret the results.