Dan Boyd is a financial planner trying to determine how to invest $$130,000$ for one of his clients. The cash flows for the five investments under consideration are summarized in the following table: Summary of Cash In$-$Flows and Out$-$Flows $($at Beginning of Year$)12345$Year $11\mathrm{.}000\mathrm{.}001\mathrm{.}000\mathrm{.}001\mathrm{.}00$Year $2+0\mathrm{.}451\mathrm{.}000\mathrm{.}000\mathrm{.}000\mathrm{.}00$Year $3+1\mathrm{.}050\mathrm{.}000\mathrm{.}001\mathrm{.}00+1\mathrm{.}25$Year $40\mathrm{.}00+1\mathrm{.}25+1\mathrm{.}70+1\mathrm{.}250\mathrm{.}00$ For example, if Dan invests $$1$ in investment $1$ 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 $$1$ in investment $2$ at the beginning of year $2$ and receive $$1\mathrm{.}25$ 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 to maximize the amount of money $($in dollars$)$ available at the end of year $4.($Let Xi be the amount to invest, in dollars, in investment i$.$ Let Mj be the amount to invest, in dollars, in the money market in year j for j $=1,2,3.$ Let Yi $=1$ if Xi $>0$ and $0$ otherwise. Enter your answers for your "minimum required investments" and linking constraints as comma$-$separated lists of inequalities and$/$or equations. In your linking constraints, use $500,000$ for each big M value.$)$ MAX: Subject to:total invested in year $1$ total available at end of year $2$ total available at end of year $3$ minimum required investments linking constraints Xi$,$ Mj $0$ and integer Yi binary $($b$)$ Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? $($X$1,$ X$2,$ X$3,$ X$4,$ X$5,$ M$1,$ M$2,$ M$3)=$