The cost in millions of dollars of building a threestory hig

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

C(x) = 2.1 + 0.14x 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 $0.17 million dollars per thousand square feet.

QUESTIONS

(a.) What is the profit function (in millions of dollars)? P(x) =

(b.) What size school should you build in order to break even? (Round your answer to 3 decimal places.)

Solution

Profit = Income -    Cost

P(x) =     R(x)   -    C(x)

Revenue function : R(x) = 0.17 *x where x is the number of thousands of square feet.

C(x) = 2.1 + 0.14x 0.0001x2

a) So, P(x) = 0.17x - (2.1 + 0.14x 0.0001x2 ) = 0.0001x^2 + 0.03x - 2.1

b) Break even when : R(x) = C(x)

0.0001x^2 + 0.03x - 2.1 =0 ; Solve for x

x = 58.567 , -358.56 ..... Neglecting -ve result

x = 58.567   thousands square feet