Problem I (AWZ 73-923 adjusted) A bank is attempting to determine where its assets should be invested during the current year. At present, $3,000,000 is available for investments in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds, 5%; home loans, 10%; auto loans, 8%; personal loans, 12%. To ensure that the banks portfolio is not too risky, the banks investment manager has placed the following three restrictions on the banks portfolio:

The amount invested in personal loans cannot exceed the amount invested in bonds.

The amount invested in home loans cannot exceed the amount invested in auto loans.

The total amount invested in bonds and auto loans combined is at most $1,200,000

No more than 20% of the total amount invested can be in personal loans.

Help the bank maximize the annual return on its investment portfolio.

Formulate this question as a Linear Programming Model. Define the variables, write the constraints, and write the objective function in mathematical (algebraic) terms (variables, inequalities, etc.).

Find the optimal solution using SOLVER.