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?
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