Homework Calculus Question

Question

A construction company finds that their costs, in dollars, for any given job follows the function c(t) = 1500t+ 2000 where t > 0 is the time in months, and the rate they charge a client for the job follows the function r(t) = 180t^2 + 100t + 2000.

(a) What is the shortest amount of time for a project they should accept if they want to be profitable? (Hint: When are the costs the same as revenue?)

(b) How much would their revenue and costs be at this time?

Answer 1

1500t + 2000 = 180t^2 + 100t + 2000

0 = 180t^2 - 1400t

0 = 18t^2 - 140t

0 = 9t^2 - 70t

0 = t(9t-70)

t=0 or t = 70/9

t = 7 and 7/9

which produces 13666 and 2/3