A construction company has an expenditure rate of E'(x) = e0.12x dollars per day on a particular paving job and an income rate of I'(x) = 120.4 - e0.12x dollars per day on the same job, where x is 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.
a) Find the optimal number of days for the job to last.
b) Find the total income for the optimum number of days.
c) Find the total expenditures for the optimum number of days.
d) Find the maximum profit for the job.