Calculus

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I don't understand how to get q for this problem? The next steps for the problem, you just need to plug q in, but I'm not sure what to do?
Do you set revenues equal to expenses?
Problem:
Revenue is given by
R(q) = 750q
and cost is given by
C(q) = 6000 + 5q2.
1) At what quantity is profit maximized?
q =
2) What is the total profit at this production level?

For problem 2, it's clear you just need to plug q in. I just don't know how to get q.
Please help?

  • Calculus -

    You find q by taking the derivatives of both R(q) and C(q) and setting the derivatives equal to each other.
    R'(q)=750
    C'(q)=10q
    q=75
    Total profit is $22125, once you plug it in.

  • Calculus -

    profit is revenue - cost
    P(q) = R(q)-C(q)
    = 750q - (6000+5q^2)
    = -5q^2 + 750q - 6000

    dP/dq = -10q + 750
    So, P is maximuzed when q=75

    revenue = cost is the break-even point. Not much profit there...

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