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21 May, 15:01

A manufacturing company has developed a cost model, C (X) = 0.15x^3 + 0.01x^2 + 2x + 120, where X is the number of item sold thousand. The sales price can be modeled by S (x) + 30 - 0.01x. Therefore revenues are modeled by R (x) = x*S (x).

The company's profit, P (x) = R (x) - C (x) could be modeled by

1. 0.15x^3 + 0.02x^2 - 28x+120

2. - 0.15x^3-0.02x^2+28x-120

3. - 0.15x^3+0.01x^2-2.01x-120

4. - 0.15x^3+32x+120

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Answers (1)
  1. 21 May, 15:22
    0
    Profit is calculated by subtracting the total cost from the total revenue as expressed in the equation given above as,

    P (x) = R (x) - C (x)

    If we are to substitute the given expression for each of the terms, we have,

    P (x) = x (S (x)) - C (x)

    Substituting,

    P (x) = x (30 - 0.01x) - (0.15x³ + 0.01x² + 2x + 120)

    Simplifying,

    P (x) = 30x - 0.01x² - 0.15x³ - 0.01x² - 2x - 120

    Combining like terms,

    P (x) = - 0.15x³ - 0.02x² + 28x - 120

    The answer to this item is the second among the choice, number 2.
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