a company\'s market research department recommends the manufacture and marketing

Question

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.

Explanation / Answer

A)

any positive value of x

B)

c'(x)=2

it means increase production by one increse cost by $2

C)TR= Quntity X price

= xp

= x(10-0.0011x)

it is appropriate for all positive value of x.

TR=10x-0.0011x^2

MR=10-0.0022x

MR at 2000

=10-0.0022(2000)

=5.6

MR at 5000

=-1

MR at 7000

=-5.4

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