Chapter 7.5, Problem 37E

Profit Canham Enterprises had an expenditure rate of $E^{\prime }\left(t\right)=e^{0.1t}$ dollars per day and an income rate of $I^{\prime }\left(t\right)=98.8-e^{0.1t}$ dollars per day on a particular job, where $t$ was the number of days from the start of the job. The company’s profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. Find the following.

a. The optimum number of days for the job to last

b. The total income for the optimum number of days

c. The total expenditures for the optimum number of days

d. The maximum profit for the job