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Math Help - Calculus Maximize Problems...

  1. #1
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    Calculus Maximize Problems...

    I don't really get the steps to take for these two problems. Thank you guys for your help!

    1.) C(q)=q375q2+1875q+1070 for 0q50 and a price per unit of $500.

    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 = $

    2.) Suppose the cost function for producing gadgets is C(q)=004q2+5q+44.

    At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer: items.

    What is the maximum profit if each item is sold for 7 dollars? Answer: dollars.
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  2. #2
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    I just realized there was some problems with my post. Sorry about that.
    Anyway, I think the #1.)answer for a:38, and b:$18,892. I don't know what to do for the rest though.

    1.) C(q)=q^375q^2+1875q+1070 for 0<q<50 and a price per unit of $500.
    ^--(These are "equal to" as well)

    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 = $

    2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

    At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

    What is the maximum profit if each item is sold for 7 dollars? Answer:
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  3. #3
    Member sinewave85's Avatar
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    Quote Originally Posted by fifinambo View Post
    I just realized there was some problems with my post. Sorry about that.
    Anyway, I think the #1.)answer for a:38, and b:$18,892. I don't know what to do for the rest though.

    1.) C(q)=q^3–75q^2+1875q+1070 for 0<q<50 and a price per unit of $500.
    ^--(These are "equal to" as well)

    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 = $

    2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

    At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

    What is the maximum profit if each item is sold for 7 dollars? Answer:
    (Edit: This was my initial response, which I quickly modified to what follows. I am putting it back because the thread does not make sense without it) Is that a cost equation or a revenue equation?

    Ok, well the calculus for this problem may be a bit advanced for me, but assuming that your answer for a) is correct, wouldn't the total revenue just be 38*500 = 19000? And that would make the total profit 19000 - 18,892 = 108.

    Edit: Ok, thinking back to my economics and using my graphing calculator, I can at least confirm the answer for a), albeit in a rather informal way. Profit occurs when total cost is less than total revenue, and in this case that only happens on the interval specified between about x = 36.199418 and x = 39.54799. The distance between the curves appears to be greatest around x = 38, and testing seems to bear this out. Profit is $71 at x = 37 and $61 at x = 39. So whatever you did to find the value for q in Problem 1 should work for Problem 2. The total profit is just (number of units sold)*(price per unit) - (total cost).
    Last edited by sinewave85; March 27th 2009 at 06:39 PM. Reason: Better answer.
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  4. #4
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    I believe it's a cost equation.
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  5. #5
    Member sinewave85's Avatar
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    Quote Originally Posted by fifinambo View Post
    I just realized there was some problems with my post. Sorry about that.
    Anyway, I think the #1.)answer for a:38, and b:$18,892. I don't know what to do for the rest though.

    2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

    At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

    What is the maximum profit if each item is sold for 7 dollars? Answer:
    On Problem 2, there appears to be no q on [0,50] for which a profit is possible, since C(q) is always greater than 7q on that interval.
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