To control water pollution and process waste sludge, an engineer for a food processing company wants to

compare the costs of the total design, construction and operation of two Options of aerobic digesters to

handle a volume rate of $10$ million gallons per day $(10$ MGD$).$

Option $1$: Model A aerobic digester, designed to handle a volume rate of $5$ MGD$,$ will have an initial

cost of $$20,000\mathrm{.}00$ for the design and construction at the start of the project, and its operating costs will be

$10\%$ of its initial cost in each of years $1$ and $2$ and then rise by $10\%$ each year thereafter. This project has

an annual interest rate of $10\%.$ Two Model A digesters will be needed to handle the desired volume rate.

Option $2$: Model B aerobic digester, designed to handle twice the volume rate of Model A$,$ has an

annual operating cost that is $3$ times the annual operating cost of a Model A digester. Only one Model B

digester is required.

a$)$ Referring to Appendix $1$ where appropriate for initial capital costs, determine the Net Present

Worth $($PW$)$ for each Option in terms of the unknown number of years, $N,$ of operation.

b$)$ Sensitivity Study of the Net Present Worth $($PW$)$ versus number of years, $N.$

Determine the breakeven point between the two Options, and plot the PW for each Option on a

single figure around the breakeven point.

c$)$ Comment on the sensitivity of the result around this breakeven point.