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Math Help - Profit while units remain constant

  1. #1
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    Profit while units remain constant

    Can anyone help me solve this problem and show me how it's done? I need it for a work seminar and am stuck in the sand

    Your Goal is to grow your profit dollars by 10% next year, but you expect no growth in unit sales. Based on this year's results shown below, assuming no changes in retail price or cost, how many units must you shift from standard products to premium products in order to achieve your goal?

    ...........................Units...............Dol lars........................Profit Dollars
    Premium Products 706,425 ........... 6,285,400................. 2,543,130
    Standard Products 625,000.............3,678,700.................. 825,000
    Total Products 1,331,425...........9,964,100...................3, 368,130
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Profit while units remain constant

    First calculate the profit per unit for both the standard and premium product lines; let's call these values P_s for "profit per unit on standard product" and P_p for profit/unit on premium product. The total profit is then:

     P_s \times Q_s  + P_p \times Q_p = Total\ Profit

    Now you want to change the quanties of standard and premium products sold, but keep the total volume the same. Let 'x' = increase in number of premium products sold, so the new quantity of premium products is Q_p+x. That means the new number of standard products sold is Q_s-x. The total profit is increased 10%, so now you have the new equation:

     P_s(Q_s-x) + P_p(Q_p+x) = 1.1 \times Total\ Profit

    Solve for x.
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