The cost c of producing t units is given by c(t)=4t^2+9t, and the revenue r generated from selling t units is given by r(t)=5t^2+t. for what values of t will there be a profit?

Profit is surplus amount from the costs and selling price

so.. in short, profit  is Revenue - Costs, whatever is left, is profit

thus the profit function or P(t) will be R(t) - C(t)

thus 

solve for "t", any value greater than 0, is profit