$5$ A small toy store, Toyco projects the monthly cash flows

$($in thousands of dollars$)$ in Table $42$ during the year $2003.$

A negative cash flow means that cash outflows exceed cash

inflows to the business. To pay its bills, Toyco will need to

borrow money early in the year. Money can be borrowed in

two ways:

a Taking out a long$-$term one$-$year loan in January. In$-$

terest of $1\%$ is charged each month, and the loan must

be paid back at the end of December.

b Each month money can be borrowed from a short$-$

term bank line of credit. Here, a monthly interest rate of

$1\mathrm{.}5\%$ is charged. All short$-$term loans must be paid off

at the end of December.

At the end of each month, excess cash earns $0\mathrm{.}4\%$ in$-$

terest. Formulate an LP whose solution will help Toyco

maximize its cash position at the beginning of January,