Question

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

Answer 1

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.