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 toasters at a price of $16 per toaster and a weekly demand of 300 toasters at a price of $14 per toaster.The financial department estimates that weekly fixed costs will be $1,400 and variable costs (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 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<=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=750 and interpret the results.