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Suppose r(x) = 8(x)^(1/2) represents revenue and c(x) = 2(x)^2 represents cost, with x measured in thousands of units. Is there a production level that maximizes profit? If so, what is it?

  • Math - ,

    profit = revenue - cost
    = 8√x - 2x^2

    d(profit)/dx = 4/√x - 4x
    = 0 for a max of profit

    4/√x = 4x
    x = 1

    since x was measured in thousands,
    they should have a production of 1000

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