Revenue, cost and profit. A company is planning to manufacture and market a new two-slice electric toaster. After

Revenue, cost and profit. A company is planning to manufacture and market a new two-slice electric toaster. After

conducting extensive market surveys, the research department provides the following estimates: A weekly demand of 200 toaster at price of $16 per toaster and a weekly demand of 300 toaster at a price of $14 per toaster. The financial department estimate that weekly fixed cost will be 1400 and variable cost (cost per unit) will be $4

(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 estimate to express the cost function in terms of x.

(D) Graph the cost function and revenue function on the same coordinate system 0 less than or equal X less than or equal 1000. 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 = 250 and x=475 and interpret results