calculus

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C(q) = q3−60q2+1200q+760 for 0 ≤ q ≤ 50 and a price per unit of $551.

Round your answers to the nearest whole number.
a) What production level maximizes profit?
q =

b) What is the total cost at this production level?
cost = $

c) What is the total revenue at this production level?
revenue = $

d) What is the total profit at this production level?
profit = $

  • calculus -

    did you check out the hints I gave on your previous post of this problem? If so, where do you get stuck?

    The ticket problem is similar. How far do you get on that one?

  • calculus -

    Profit = Revenue - Cost
    P = -q^3 + 60 q^2 +(-1200+551)q - 760

    dp/dq = -3 q^2 +120q - 649
    zero for max or min
    q^2 - 40 q + 216.333... = 0

    q = [ 40 +/-sqrt (1600-865)]/2
    q = [40+/-27.1)/2
    q = 34 or 6.5
    to find out if max or min, take next derivative
    d^2p/dq^2 = -6q +120
    at q = 34
    this is -84, so a maximum
    at q = 6.5
    this is +81 so a minimum
    so for maximum profit we want q = 34
    I think you can do the rest, check my arithmetic

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