Question

He cost, in millions of dollars, of building a three-story high school in new york state was estimated to be c(x) = 2.1 + 0.12x − 0.0001x2 (20 ≤ x ≤ 400) where x is the number of thousands of square feet. suppose that you are contemplating building a for-profit three-story high school and estimate that your total revenue will be $0.2 million dollars per thousand square feet. what is the profit function (in millions of dollars)?

Answer 1

Given cost function is

c(x) =
`2.1 + 0.12x - 0.0001x^2` (20 ≤ x ≤ 400)

where x is the number of thousands of square feet

total revenue will be $0.2 million dollars per thousand square feet

Revenue is 0.2 millions per thousand square feet. we know x is the number of thousand of square feet

So R(x) = 0.2x

We know Profit = Revenue - Cost

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

`P(x) = 0.2x - (2.1 + 0.12x - 0.0001x^2)`

`P(x) = 0.2x - 2.1 - 0.12x + 0.0001x^2)`

combine like terms

`P(x) =-2.1 + 0.08x + 0.0001x^2`

Profit function is

`P(x) =0.0001x^2 + 0.08x - 2.1`