6 A company must meet the following demands for cash at the beginning of each of the next six months: month 1,

$200; month 2, $100; month 3, $50; month 4, $80; month 5, $160; month 6, $140. At the beginning of month 1, the company has $150 in cash and $200 worth of bond 1, $100 worth of bond 2, and $400 worth of bond 3. The company will have to sell some bonds to meet demands, but a penalty will be charged for any bonds sold before the end of month 6. The penalties for selling $1 worth of each bond are as shown in Table 63.
a Assuming that all bills must be paid on time, formulate a balanced transportation problem that can be

used to minimize the cost of meeting the cash demands for the next six months.
b Assume that payment of bills can be made after they are due, but a penalty of 5¢ per month is assessed for each dollar of cash demands that is postponed for one month. Assuming all bills must be paid by the end of month 6, develop a transshipment model that can be used to minimize the cost of paying the next six months’
bills. (Hint: Transshipment points are needed, in the form Ct cash available at beginning of month t after bonds for month t have been sold, but before month t demand is met. Shipments into Ct occur from bond sales and Ct 1. Shipments out of Ct occur to Ct 1 and demands for months 1, 2, . . . . t.)

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TABLE 62 To ($) New York From Denver Detroit 1,253 637 Atlanta 1,398 841 To ($) From Los Angeles Chicago Philadelphia Denver 1,059 996 1,691 New York 2,786 802 100