A company's market research department recommends the manufacture and marketing of a new headphone set for MP3 players. After suitable test marketing, the research department suggests a demand function of x = 10,000 - 1000p, where x is the number of sets demanded at price Sp. The financial department estimates the cost function as C(x) = 7000 + 2x, where S7000 is the estimate of fixed costs and $2 is the estimate of variable costs per set 4. Find the domain of the demand function. 5. Find and interpret the marginal cost function. 6. Find the revenue function as a function of x. State the domain. (Remember that revenue is number of units x price per unit.) How many sets should be sold for maximum revenue? 7. Find the marginal revenue at x 2000. Interpret the answers. 8. Graph the cost function and the revenue function in the same coordinate system. Find the intersection point(s) and explain what the point(s) mean(s). 9. Find the profit function and its domain. Sketch the graph of the function. How many sets should be sold for maximum profit? 10. Find the marginal profit at x 1000. Interpret the answers