Question

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?

Answer 1

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
`\bf \begin{cases} R(t)=5t^2+t\\\\ C(t)=4t^2+9t \end{cases}\qquad \begin{array}{llll} P(t)=(5t^2+t)\quad -\quad (4t^2+9t)\\\\ P(t)=5t^2-4t^2+t-9t\\\\ P(t)=t^2-8t \end{array}`

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