Based on Sartoris and Spruill XXXXXXXXXXWivco produces two products, which it sells on both a cash and credit basis. Revenues from credit sales will not have been received but are included in...

Based on Sartoris and Spruill (1974). Wivco produces two products, which it sells on both a cash and credit basis. Revenues from credit sales will not have been received but are included in determining profit earned during the current 6-month period. Sales during the next 6 months can be made either from units produced during the next 6 months or from beginning inventory. Relevant information about products 1 and 2 is as follows.


■ During the next 6 months, at most 150 units of product 1 can be sold on a cash basis, and at most 100 units of product 1 can be sold on a credit basis. It costs $35 to produce each unit of product 1, and each sells for $40. A credit sale of a unit of product 1 yields $0.50 less profit than a cash sale (because of delays in receiving payment). Two hours of production time are needed to produce each unit of product 1. At the beginning of the 6-month period, 60 units of product 1 are in inventory.


■ During the next 6 months, at most 175 units of product 2 can be sold on a cash basis, and at most 250 units of product 2 can be sold on a credit basis. It costs $45 to produce each unit of product 2, and each sells for $52.50. A credit sale of a unit of product 2 yields $1.00 less profit than a cash sale. Four hours of production time are needed to produce each unit of product 2. At the beginning of the 6-month period, 30 units of product 2 are in inventory.


■ During the next 6 months, Wivco has 1000 hours for production available. At the end of the next 6 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 6-month period.

a.  Develop and solve an LP model that yields Wivco’s maximum profit during the next 6 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 6-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




Assuming initially that current liabilities equal $150, 6 months from now Wivco’s current ratio will equal




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.