1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Ahhh Applied Calc problem, i need an answer by 2am, thats when it is due HELP!

  1. Nov 19, 2004 #1
    Ahhh!!! Applied Calc problem, i need an answer by 2am, thats when it is due!!!! HELP!

    the cost of producing q goods = .4q^2 + 10q

    the marginal cost is given by the derivative, .8q + 10

    what is the maximum profit if each item is sold for 19 dollars (assume you sell everything you produce)
  2. jcsd
  3. Nov 19, 2004 #2
    set up the profit function (income minus costs) and then take the derivative of the whole thing and set it equal to zero. looking at marginal cost separately is not that useful (though, of course, by taking the derivative of the whole thing and setting it equal to zero you'll be looking for that magic point where the marginal cost and marginal profit are equal)
  4. Nov 19, 2004 #3
    profit=price of producing q goods-cost of producing q goods =>

    profit= 19(q)-(.4q^2 +10q) =9(q)-.4q^2 from here you need either to find the vertex of this parabola or to derivate for its maximum.
  5. Nov 19, 2004 #4


    User Avatar
    Science Advisor

    Since you are given the marginal cost, the maximum profit occurs when the price of the item equals the marginal cost. (Producing one more would make the cost greater than the price and you start losing money.)

    That is .8q+ 10= 19. Solve that for q and then find:
    1) income: 19q
    2) cost .4q^2 + 10q
    3) Subtract to find profit.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook