$45.$ Moneyco has $\backslash (\backslash$$ $1000\backslash )$ to invest at time $1($the beginning of year $1).$ The cash flows associated with the five availahle investments are described in Thble $4\mathrm{.}22.$ For example, every dollar invested in A at time $1$ yields $\backslash (\backslash$$ $1\mathrm{.}40\backslash )$ at time $4.$ In addition to these investments, Moneyco can invest as much money each year as it wants in CDs$,$ which pay $\backslash (6\backslash \%\backslash )$ interest. The company wants to maximize its available cash at time $4.$ Assuming it can put no more than $\backslash (\backslash$$ $500\backslash )$ in any investment, formulate an L$.$P model to help Moneyco achieve its goal.