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Calculus

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The perfect pizza parlor estimates the average daily cost per pizza to be C(x) = (0.00025x^2 + 8x + 10)/x , where x is a number of pizzas made in a day.

a) determine the total cost at the level of production of 50 pizzas a day.

b) determine the production level that would minimize the average daily cost per pizza.

c) what is the minimum average daily cost per pizza?

  • Calculus - ,

    cost per pizza at x = 50 is
    [.00025(50)^2 + 8(50) +10 ]/50 = 8.21
    * 50 = 410.63

    dc/dx = [x (.0005 x + 8) -.00025x^2-8x-10) ]/x^2
    when is the numerator zero?
    .0005 x^2 + 8 x -.00025 x^2 -8 x -10 = 0
    .00025 x^2 = 10
    x = 200

    for c, use 200 for x

  • Calculus - ,

    (a) Plug in 50 for x and compute C(x).
    (b) Solve for the value of x for which
    C'(x) = dC(x)/dx = = 0.00025 x -20/x
    = 0
    25x^2 = 20,000

    (c) Compute C(x) using the value of x from (b)

  • Calculus - ,

    thanks :)

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