Paperbank is starting a new credit card business operation during the next three months (Jan, Feb, and March). It must decide how many credit cards to issue each month. Two kinds of cards will be issued: regular and gold. The profit will be $50 per month for gold cards, and $20 per month for regular cards. In each month, 5% of the regular cards and 20% of the gold cards will have late payments.

The size of the bank's operation will increase during the next three months. It's data processing unit will only be able to keep track of 9000 cards in January. This will increase to 11,000 in February to 13,000 in March. The bank does not want to have more than 300 late cards in January, 600 in February, and 900 in March. The company must decide how many credit cards of each kind to issue in each month. It wants to maximize its total profit during the three months.

• Formulate a linear programming model of the problem.
• Describe the optimal solution within the context of the problem.