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 presents the following price demand equation p = 10 -0.001x where x the number of headphones that retailers that retailers are likely to buy at $p per set. The financial department provides the cost function C(x) = 7,000 + 2x where @7,000 is the estimate of fixed costs (tooling and overhead) and $2 is the estimate of variable cost per headphone set (materials, labor, marketing, transportation, storage, etc.). Given the price demand equation, for what values of x is it appropriate? Find and interpret the marginal cost function C'(x). Find the revenue function as a function of x. For what values of x is it appropriate? Find the marginal revenue at x = 2,000, 5,000, and 7,000. Interpret these results. Graph the cost function and the revenue function in the same coordinate system. Find the intersection points of these two graphs and interpret the results. Find the profit function and sketch the graph of the function. For what values of x is it appropriate? Find the marginal profit at x = 1,000, 4,000, and 6,000. Interpret these results. Describe the graph of f(x) = 2x/1 + x^2 in terms of our 14 descriptors. Solve the equation x^3 - 3x^2 = -2 using DESMOS for approximate answers and Wolfram for exact answers. A cow weighing 300 pounds gains 8 pounds per day, and costs $0.60 a day to keep. The market price for beef is $0.75 per pound, but is falling $0.01 per day. When should the cow be sold to maximize profit? A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plant for production of the primer. How many times a year should the company produce this prime in order to minimize the total storage and setup costs