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Profit function

  1. Sep 19, 2009 #1
    Profit function!!!

    Problem: A company is considering selling a new line of widgets at a special promotional price of $49. If the cost of setting up the manufacturing process is $2500, an each widget costs $32.35 to produce, how many should the company sell in order to realise a profit of at least $7000? If the cost of manufacturing increases by $2.75, how many widgets must be sold at the original selling price to obtain the same profit?

    Here is what I have done:

    R(x) = 49x
    C(x)=$2500+$32.35x
    P(x)= -2500+16.65x

    If P(x) =$7000, then
    7000= -2500+16.65x
    7000+2500=16.65x
    9500 =16.65x
    9500/16.65 = x
    x = 570.57....

    If costs increases by $2.75, then
    C(x) = 2500 + 35
    P(x)-C(x) = -2500 + 14x
    If P(x) = $7000, then

    7000= -2500+14x
    7000+2500 = 14x
    9500/14 = x
    x=678.57...

    Can anyone double check this answer for me or tell me if I am completly lost???
    Thank you in advance
     
  2. jcsd
  3. Sep 19, 2009 #2
    Re: Profit function!!!

    Looks correct to me. The equationf produces a higher result when the cost to manufacture the widget increases.

    Thanks
    Matt
     
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