Question

A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over afifteen-year period. The company represents its revenue and costs as a function of time, in years, x,using the given functions.R(x) 550x3 - 12,000x2 + 83,000x + 7000C(x) 880x3 - 21,000x2 + 150,000x - 160,000The company’s profits can be represented as the difference between its revenue and costs.Write the profit function, P(x), as a polynomial in standard form.

Answer 1

The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, P(x) = -330
`x^3` + 9,000
`x^2` - 67,000x + 167,000.

Step-by-step explanation:

The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, we have:

R(x) = 550
`x^3` - 12,000
`x^2` + 83,000x + 7000

C(x) = 880
`x^3` - 21,000
`x^2` + 150,000x - 160,000

To find P(x), we subtract C(x) from R(x):

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

Substituting the given functions, we get:

P(x) = (550
`x^3` - 12,000
`x^2` + 83,000x + 7000) - (880x3 - 21,000
`x^2` + 150,000x - 160,000)

Simplifying, we combine like terms:

P(x) = -330
`x^3` + 9,000
`x^2` - 67,000x + 167,000

Therefore, the profit function, P(x), can be expressed as a polynomial in standard form as -330
`x^3` + 9,000
`x^2` - 67,000x + 167,000.

Answer 2

`P(x) =-330\cdot x^(3) +9000\cdot x^(2)-67000\cdot x + 167000`

Step-by-step explanation:

The profit function is computed by using the following expression:

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

`P(x) = 550\cdot x^(3) - 12000\cdot x^(2) + 83000\cdot x + 7000 - 880\cdot x^(3) + 21000\cdot x^(2) - 150000\cdot x + 160000`

`P(x) = (550-880)\cdot x ^(3) + (-12000+21000)\cdot x^(2)+(83000-150000)\cdot x + (7000+160000)`

`P(x) =-330\cdot x^(3) +9000\cdot x^(2)-67000\cdot x + 167000`