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=10-0.0011x where x is the number of headphones 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 costs per headphone set (materials,labor, marketing, transporation,storage, etc).
A- given the price demand equation for what values of x is it appropriate?
B- fina and interpret the marginal cost function c' (x)
C- find the revenue function as a function of x. for what values of x is it appropriate?
D- find the marginal revenue at x=2,000,5,000, and 7,000. interpret these results
E-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.
F-find the profit function and sketch the graph of the function. for what values of x is it appropriate?
G- find the marginal profit at x=1,000,4,000, and 6,000. interpret these results.