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Math

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The weekly demand for the Pulsar 25-in. color console television is given by the demand equation

p=-0.05x+502 (0(less than or equal too)x(less than or equal too)12,000)

where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by

c(x)=0.000003x^3-0.05x^2+400x+80,000

where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest whole number.)

? units

  • Math -

    profit = revenue - cost
    revenue = price * quantity

    profit is thus

    y = x(-0.05x+502) - (0.000003x^3-
    0.05x^2+400x+80000)
    y = 0.000003x^3 + 102x + 80000

    y' = -0.000009x^2 + 102
    y'=0 when x = 3366

  • Math -

    how did you get 3366?

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