At the beginning of the six-month period, 30 units of product 2 are in inventory.

■ During the next six months, Wivco has 1000 hours for production available. At the end of the next six months, Wivco incurs a 10% holding cost on the value of ending inventory (measured relative to production cost). An opportunity cost of 5% is also assessed against any cash on hand at the end of the six-month period.

a. Develop and solve an LP model that yields Wivco’s maximum profit during the next six months. What is Wivco’s ending inventory position? Assuming an initial cash balance of $0, what is Wivco’s ending cash balance?

b. Because an ending inventory and cash position of

$0 is undesirable (for ongoing operations), Wivco is considering other options. At the beginning of the six-month period, Wivco can obtain a loan

(secured by ending inventory) that incurs an interest cost equal to 5% of the value of the loan. The maximum value of the loan is 75% of the value of the ending inventory. The loan will be repaid one year from now. Wivco has the following goals (listed in order of priority):

■ Goal 1: Make the ending cash balance of Wivco come as close as possible to $75.

■ Goal 2: Make profit come as close as possible to the profit level obtained in part a.

■ Goal 3: At any time, Wivco’s current ratio is defined to be Current ratio 
Assuming initially that current liabilities equal $150, six months from now Wivco’s current ratio will equal Current ratio 
where CB is the ending cash balance, AR is the value of accounts receivable, and EI is the value of the ending inventory. Six months from now, Wivco wants the current ratio to be as close as possible to 2.
Use goal programming to determine Wivco’s production and financial strategy.
Modeling Problems