Chapter 4.4, Problem 45E

Total and average daily profit. Great Green, Inc., deter-mines that its marginal revenue per day is given by

$R\text{'}\left(t\right)=75e^t-2t,R\left(0\right)=0,$

where $R\left(t\right)$ is the total accumulated revenue, in dollars, on day $t$.

The company’s marginal cost per day is given by $C\text{'}\left(t\right)=75-3t,C\left(0\right)=0,$

where $C\left(t\right)$ is the total accumulated cost, in dollars, on day $t$.

a) Find the total profit from $t=0tot=10$.

Note:

$P\left(T\right)=R\left(T\right)-C\left(T\right)={\displaystyle {\int }_0^T\left[R\text{'}\left(t\right)-C\text{'}\left(t\right)\right]dt}$

b) Find the average daily profit for the first 10 days.