Kate Warner, a senior loan officer with Citybank in Cleveland, Ohio, has both corporate and personal lending customers. On average, the profit contribution margin or interest rate spread is 1.5 percent on corporate loans and 2 percent on personal loans. This return difference reflects the fact that personal loans tend to be riskier than corporate loans. Warner seeks to maximize the total dollar profit contribution earned, subject to a variety of restrictions on her lending practices. To limit default risk, Warner must restrict personal loans to no more than 50 percent of the total loans outstanding. Similarly, to ensure adequate diversification against business-cycle risk, corporate lending cannot exceed 75 percent of loaned funds. To maintain good customer relations by serving the basic needs of the local business community, Warner has decided to extend at least 25 percent of her total credit authorization to corporate customers on an ongoing basis. Finally, Warner cannot exceed her current total credit authorization of $100 million.

A. Using the inequality form of the constraint conditions, set up and interpret the linear programming problem that Warner would use to determine the optimal dollar amount of credit to extend to corporate (C) and personal (P) lending customers. Also formulate the LP problem using the equality form of the constraint conditions.

B. Use a graph to determine the optimal solution, and check your solution algebraically. Fully interpret solution values.