Q$4$: Chapter $3,$ Problem $41$

Please download the Excel file for your work and submit your Excel file.

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.

If Jack invests $$1$ in investment $A$ at the beginning of year $1,$ he will receive $$0\mathrm{.}50$ at the beginning of year $2$ and another $$0\mathrm{.}80$ at the beginning of year $3.$ Alternatively, he can invest $$1$ in investment B at the beginning of year $2$ and receive $$1\mathrm{.}25$ at the beginning of year $4.$ Entries of $""$ in the table indicate times when no cash inflows or outflows can occur. At the beginning of any year, Jack can place money in a money. market account that is expected to yield $8\%$ per year. He wants to keep at least $$50,000$ in the money market account 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.

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

c$.$ What is the optimal solution?