C(x)= cost to manufacture C\'(x)=marginal cost (Rate at which cost is increasing
ID: 2886810 • Letter: C
Question
C(x)= cost to manufacture C'(x)=marginal cost (Rate at which cost is increasing as the xth items is produced)
p(x)=demand function (price function)
R(x)= revenue function (quantity x price) = x*p(x)
R'(x)=marginal revenue function (rate of change of revenue wrt # units sold)
If x units are sold, P(x)=R(x)-C(x)
P(x)=profit function
P'(x)=marginal profit function
If p(x)=5-0.002x and C(x)=3+1.10x. Find the marginal revenue, marginal cost, and marginal profit. Determine the production level that will produce the maximum total profit.
THANK YOU!!!!
Explanation / Answer
given p(x)=5-0.002x and C(x)=3+1.10x
R(x)= x*p(x)
=>R(x)= x(5-0.002x)
=>R(x)= (5x-0.002x2)
marginal revenue=R'(x)
marginal revenue=(5*1 -0.002*2x2-1)
marginal revenue=5 - 0.004x
marginal cost =C'(x)
marginal cost =(0+1.10*1)
marginal cost =1.10
marginal profit=marginal revenue-marginal cost
marginal profit=5 -0.004x -1.10
marginal profit=3.9 -0.004x
production level will produce the maximum total profit when marginal profit is 0
=>3.9 -0.004x =0
=>x=3.9/0.004
=>x=975
production level of 975 items will produce the maximum total profit
please rate if helpful. please comment if you have any doubt
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.