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Terry makes and sells necklaces. He has observed over time that when the price is $12 each, he sells an average of 20 per day. If he increases the price, then his average sales fall by 2 per day for each dollar increase. The materials for each necklace cost $7. Express his profit P as a function of x, the number of necklaces sold.

that would make p(x)= ?


  • math -

    at price z, demand
    x = 20-2(z-12)
    or, price z = 22 - x/2

    p(x) = revenue-cost
    = x(22 - x/2) - 7x
    = 15x - 1/2 x^2

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