Integral Exercise:

Suppose a firm produces a good and you know a few things:

Fact 1: Marginal Revenue equals 44-5Q

Fact 2: when the firm sells nothing, Q=0, its total revenue equals 0$. this is helpful for thinking about the constant term for revenue (hint, this is an indefinite integral with a constant term).

Fact 3: Marginal Cost equals 3Q+20

Fact 4: when the firm produces Q=80, total cost equals 11,400$. this is helpful for thinking about the constant term for costs (hint: another indefinite integral).

With these four facts, use integration to solve for three functions: total revenue (TR(Q)), total costs (TC(Q)), and total profits.