Problem $31$: Dan Boyd is a financial planner trying to determine how to invest

$$100,000$ for one of his clients. The cash flows for the five investments under

consideration are summarized in the following table:

For example, if Dan invests $$1$ in investment A at the beginning of year $1,$ he

will receive $$0\mathrm{.}45$ at the beginning of year $2$ and another $$1\mathrm{.}05$ at the beginning

of year $3.$ Alternatively, he can invest $$1$ in investment B at the beginning of

year $2$ and receive $$1\mathrm{.}30$ at the beginning of year $4.$ Entries of $0\mathrm{.}00$ in the

preceding table indicate times when no cash in$-$flows or out$-$flows can occur.

The minimum required investment for each of the possible investments is

$$50,000.$ Also, at the beginning of each year, Dan may also place any or all of

the available money in a money market account that is expected to yield $5\%$ per

year. How should Dan plan his investments if he wants to maximize the amount

of money available to his client at the end of year $4?$

a$.$ Formulate an ILP model for this problem.

b$.$ Create a spreadsheet model for this problem and solve it using Solver.

c$.$ What is the optimal solution?