Jack Potts recently won $$1,000,000$ in Las Vegas and is trying to determine how to invest his winnings. He has narrowed his decision down to five investments, which are summarized in the following table.Husni A$.$ ChantP Find $-$ c ReplaceL Select $-$ Editing$2.$ Share$($at the beginning of years$)312-10\mathrm{.}500\mathrm{.}801\mathrm{.}25-1+11\mathrm{.}351\mathrm{.}1311\mathrm{.}27$Summary of Cash Inflows and OutflowsIf Jack invests SI in investment A at the beginning of year $1,$ he will receive S$0\mathrm{.}50$ at the beginning of year $2$ and another $$0\mathrm{.}80$ at the beginning of year $3.$ Alternatively, he can invest S$1$ in investment B at the beginning of year $2$ and receive $$1\mathrm{.}25$ at the beginning of year A$.$Entries of$""$ in the table indicate times when no cash inflows or autflows can occur. At the beginning of any year, Jack can place money in a money market account that is expected to yield $8\%$ per year. He wants to keep at least $$50,000$ in the money market account at all times and doesn't want to place any more than $$500,000$ in any single investment. How would you advise Jack to invest his winnings if he wants to maximize the amount of money he'll have at the beginning of year $4?$a$.$ Formulate an LP model for this problem.