A textile manufacturer has to plan its cash flow for the coming winter season. It is known that pre-season stocking would require large cash outflows during the September-November period, while in season sales usually lead to large cash inflows in the December-January period. Expected cash flows are displayed in the following table (in units of $ 1000).

Three borrowing tools may be employed in meeting short term cash needs: Open credit account with notes receivable as collateral: Through this method, the company may borrow from its bank, up to 75% of the coming month's notes receivable total(e.g, in August up to 525 $) by showing those notes receivable as collateral. The duration of the loan is one month and its interest rate is 1.5% per month. Delayed payment (one month) in purchase of goods: Through this method, the company may pay the full cost of merchandise purchased in one month, the next month. However, in this case, they will lose the 3 % price reduction associated with cash payments( Amounts given in the table reflect 3% deducted cash payment amounts). Six-month, fixed term credit with company general assets as collateral: Through this method, the company may borrow from its bank, up to $800,000, by showing its general assets as collateral. The duration of this loan is fixed at six months and its interest rate is 1.0% per month. However, it can only be applied for and obtained at the beginning of August to be repaid at the beginning of February; it cannot be increased or decreased during the planning period. Each month, the company may invest its short-term cash surplus, generated during the month, in government bonds, which have an interest rate of 0.5% per month and may be cashed in anytime. Assume that all monetary transactions (such as getting credit, payment for purchases, payment of interest, surplus of or need for cash in commercial activities, investment in government bonds) associated with any month occur at the beginning of the month. Under these conditions, prepare a cash flow management and planning system, which will maximize end of period assets. a) Write the LP model in detail for each month and overall end of period.

\begin{tabular}{lrrrrrr} & 1. Aug. & 2. Sept. & 3. Oct. & 4. Nov. & 5. Dec. & 6. Jan. \\ \cline { 2 - 6 } Notes Receivable & 700 & 500 & 700 & 1000 & 1200 & 500 \\ Purchasing (cash payments) & 800 & 1000 & 1000 & 600 & 400 & 400 \\ Cash Needs of Com. Activities & - & 300 & 600 & 900 & - & - \\ Cash Surplus of Com. Activities & 200 & - & - & - & 300 & 1500 \end{tabular}