Formulate an algebraic model for this LP problem (define the decision variables, identify the objective function and each of constraints, and provide a model in a complete form).

The task consists of writing a repair formula by hand and solving it using an accelerator.

Problem 1. Problem 1 ( 30 points). Yonsei Bank issues five types of loans. In addition, to diversify its portfolio, and to minimize risk, Yonsei invests in risk-free securities. The loans and the risk-free securities with their annual rate of return are given in the following table. Yonsei's objective is to maximize the annual rate of return on investments subject to the following policies, restrictions, and regulations. 1. Yonsei has $90 million in available funds. 2. Risk-free securities must contain at least 10 percent of the total funds available for investments. 3. Home improvement loans cannot exceed $8,000,000. 4. The investment in home mortgage loans must be at least 60 percent of all the funds invested in loans. 5. The investment in home mortgage loans A must be at least twice as much as the investment in home mortgage loans B. 6. Home improvement loans cannot exceed 40 percent of the funds invested in home mortgage loans A. 7. Automobile loans and home improvement loans together may not exceed the commercial loans. 8. Commercial loans cannot exceed 50 percent of the total funds invested in home mortgage loans. Formulate an algebraic model for this LP problem (define the decision variables, identify the objective function and each of constraints, and provide a model in a complete form)