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

Question

Mathematics

Chippy

14 November, 00:13

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

+4

Answers (1)

Know the Answer?

Randy Nelson · 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.