A particular notbook computer has a linear price/demand function of p(n)=1190-36

Question

A particular notbook computer has a linear price/demand function of p(n)=1190-36n dollars, where n is the number in thousands of computers sold in the market. The manufacturer's fixed cost of operations is 4320 dollars while the variable cost of production is 146 per computer. What is the revenue function, R(n), in thousands of dollars? What is the total cost function, C(n), also in thousands of dollars?What is the profit function, P(n) of this manufacturer? What are the profit break even point? At what levels of sales does maximum revenue occur? At what level of sales does maximun profit occur?

Explanation / Answer

R(n)=n*P(n)=1190*n-36*n^2

cost function=4320+146*n

profit function=revenue-cost=-36*n^2+1044*n-4320

for break even point,profit=0

-36*n^2+1044*n-4320=0

n=24 or n=5

maximum revenue:

R'(n)=0

1190-72*n=0

n=16.52

so revenue for n=16,is 9824

revenue for n=17 is 9826

so maximum revenue occurs for n=17.

for maximum profit,

P'(n)=0

-72*n+1044=0

n=14.5

for n=14,profit=3240

for n=15,profit=3240

so maximum profit occurs for both n=14 and n=15

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