Western Community Bank has $1,875,000 in funds that it is allocating to various types of loans: personal loans, student loans, small-business loans. Assume that the annual rates of return are 9% for the personal loans, 10% for the student loans, and 7% for the small-business loans. The amount allocated to the student loans must be atmost 60% of the amount allocated to the personal loans. Assume that the small-business loans must have at least 35% of the available funds. The bank wishes to determine the amount that should be allocated to each type of loan to maximize the total annual return on the funds

part a) For the application described above, develop a complete LP model below, with decision variables, objective function and constraints.

part b) Proceed to create a spreadsheet model

part c) Solve the LP for the optimal solution and provide the optimal solution

part e) Without re-solving the optimization problem with different inputs, if the fund amount decreased to $1,500,000, what would be the new total annual return on the funds. Explain how you arrived at your answer.