Question

The U-Save Loan Company is planning its operations for the next year. The company makes four types of loans, listed below, together with the annual return (in percent) to the company. Legal requirements and company policies place the following limits on the various types of loans. Signature loans may not exceed 10 percent of the total amount of loans. The amount of signature and furniture loans together may not exceed 20 percent of the total amount of loans. First mortgages must be at least 40 percent of the total mortgages and at least 20 percent of the total amount of loans. The company can lend a maximum of 1.5 million dollars next operating period. Type Annual Return (percent) Signature loan 15 Furniture loan 12 Second Home Mortgage 10 First Home Mortgage 7 U-Save wants to know the amounts it should invest in each type of loan to maximize its total annual return. Formulate this problem as a linear programming problem and solve it using MS Excel Solver.

Answer 1

To maximize the total annual return, you can formulate the problem as a linear programming problem using the objective function and the given constraints. Use MS Excel Solver to solve the problem.

Step-by-step explanation:

To formulate the problem as a linear programming problem, we need to set up the objective function and constraints. Let's define the decision variables as x1, x2, x3, and x4 for signature loans, furniture loans, second home mortgages, and first home mortgages respectively.

The objective function to maximize the total annual return can be written as:

Maximize: 0.15x1 + 0.12x2 + 0.10x3 + 0.07x4

The constraints can be written as:

• x1 + x2 + x3 + x4 ≤ 1.5 million (Total amount of loans)
• x1 ≤ 0.1 * (x1 + x2 + x3 + x4) (Signature loans ≤ 10% of total loans)
• x1 + x2 ≤ 0.2 * (x1 + x2 + x3 + x4) (Signature loans + Furniture loans ≤ 20% of total loans)
• x4 ≥ 0.4 * (x3 + x4) (First home mortgages ≥ 40% of total mortgages)
• x4 ≥ 0.2 * (x1 + x2 + x3 + x4) (First home mortgages ≥ 20% of total loans)

You can use MS Excel Solver to solve this linear programming problem by setting the objective function and constraints, and running the solver.