Consider the Fun Toys example $($Dynamic Financial Model$)$ discussed in class with the following

modification. Each month Fun Toys can delay payments on some or all of the cash owed $($i$.$e$.,$ cash out$-$flow$)$

for the current month. This is called payment stretching. Payments can be stretched for only one month, and

a $1\%$ penalty is charged on the amount stretched. For example, if Fun Toys stretched $$6,000$ out of the

$$12,000$ it owes in January, it must pay $$6,000$ in January and $$6,060(=6,000\backslash$times $1\mathrm{.}01)$ in February; if it stretched

all the $$4,000$ it owes in May, it needs to pay nothing in May but must pay $$4,040(=4,000\backslash$times $1\mathrm{.}01)$ in June.

With this modification, determine how Fun Toys can maximize its final cash balance in January of the next

year. $($Note: Payment stretching is possible only for months where cash flow is negative. Payments on loans

cannot be stretched.$)$