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Math Help - Business Homework Problem Help

  1. #1
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    Apr 2009
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    Hey all, new here. This math problem is killing me, and I have to turn it in tomorrow, but I can't figure out the right answer:

    The marketing manager of a department store has determined that revenue, in dollars, is related to the number of units of television advertising x and the number of units advertising y by the function:
    R(x,y)= 250(6828x+2330y+10xy-2x^2)
    Each unit of television advertising costs $2300, and each unit of news paper advertising costs $800. If the advertising budget is $24100, find the max revenue.

    Im pretty sure the equation is:
    250(6828x+2330y+10xy-2x^2)+λ(2300x-800y-24100)


    The section is "Lagrange Multipliers". I cant get a whole number answer. Heres what I'm doing:

    Equation:250(6828x+2330y+10xy-2x^2)+λ(2300x-800y-24100)

    Derive-F(x)=250(6828+10y-4x)+2300λ
    λ=(-5/46)(6828+10y-4x)
    Derive-F(Y)=250(2330+10x)+800λ
    λ=(-5/16)(2330+10x)

    So..(-5/46)(6828x+10y-4x)=(-5/16)(2330+10x)

    Thats as far as I can go before it gets sketchy. I know you need to solve for X or Y, then substitute into 2300x+800y-24100 and solve again for both x and y

    -----------------------------------------------------------------------------------

    This problem is from a program that we have to do online, where you get 15 problems like this one, and you get 2 strikes. So i've been working on these 15 for like an hour and a half. This is problem number 15, and I have 2 strikes. So if I get this wrong, then I have to start over. And of course I dont know how to do this one... so i might be done for. Help me out guys! Thanks in advance
    Last edited by mr fantastic; April 28th 2009 at 05:06 AM. Reason: Merged posts
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