$4$

$2$

$.$

$$Jack Potts recently won $

$1$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

$$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.

$$ Summary of Cash Inflows and Outflows

$($

at beginning of years

$)$

$$

If Jack invests $

$1$

$$in investment A at the beginning of year

$1$

$,$

$$he will receive $

$0$

$.$

$5$

$0$

$$at the beginning of year

$2$

$$and another $

$0$

$.$

$8$

$0$

$$at the beginning of year

$3$

$.$

$$Alternatively$,$ he can invest $

$1$

$$in investment B at the beginning of year

$2$

$$and receive $

$1$

$.$

$2$

$5$

$$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 $

$5$

$0$

$,$

$0$

$0$

$0$

$$in the money market account at all times and doesn't want to place any more than $

$5$

$0$

$0$

$,$

$0$

$0$

$0$

$$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

$4$

$?$

Formulate an LP model for this problem.

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

What is the optimal solution?