Please help before 1155 PM The cost in millions of dollars o

Please help before 11:55 PM!!!

The cost, in millions of dollars, of building a three-story high school in New York State was estimated to be

C(x) = 2.3 + 0.15x 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 $0.18 million dollars per thousand square feet. What is the profit function (in millions of dollars)? What size school should you build in order to break even? (Round your answer to 3 decimal places.)

Solution

Cost of the building
c(x)=2.3+0.15X-0.0001*X^2 dollars

Revenue
r(x)=0.18X dollars

So Profit = Revenue - cost of building

P(x)= r(x) - c(x)

p(x) = 2.3 + 0.15X - 0.0001*X^2 - 0.18X

p(x) = 2.3 - 0.03X - 0.0001*X^2

In order to break even means to make neither a profit nor a loss. Thus, break even occurs when P(x) = 0

0 = 2.3 - 0.03X - 0.0001*X^2

Solving the cuadratic equation the results are

x1= 63.307
x2= -363.31

Replacing the positive value in our equations we have:

c(63.307) = 2.3 + 0.15(63.307) - 0.0001*(63.307)^2
c(63.307) = 11.395

p(63.307) = 2.3 - 0.03(63.307) - 0.0001*(63.307)^2
p(63.307) = 0 (no profit and no loss)