Provide: LP model $($including definition of variables$),$

optimal solution, optimal objective value$)$

winstonco is considering investing in three projects. if we fully invest in a project, the realized cash flows $($in millions of dollars$)$ will be shown in table $44.$ For example, project $1$ requires cash outflow of $$3$ million today and returns $$5\mathrm{.}5$ million $3$ years from now. Today we have $$2$ million in cash. At each time point $(0,\mathrm{.}5,1,1\mathrm{.}5,2,$ and $2\mathrm{.}5$ years from today$)$ we may, if desired borrow up to $$2$ million at $3\mathrm{.}5\%($per $6$ months$)$ interest. Leftover cat ears $3\%($per $6$ months$)$ interest. For example, if after borrowing and investing at time $0$ we have $$1$ million we would receive $$30,000$ in interest at time $\mathrm{.}5$ years. Winstonco's goal is to maximize cash on hand after it accounts for time $3$ cash flows. What investment and borrowing strategy should be used? Remember that we may invest in a fraction of a project. For example, if we invest in $\mathrm{.}5$ of project $3,$ then we would have cash outflows of $-$$$1$ million at time $0$ and $\mathrm{.}5.$