A bank has $650,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%, car loans 9.5%, and personal loans 12.5%. To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than the 25% of the total portfolio. The bank also wants to ensure that more money is invested in mortgages than personal loans. The bank also wants to invest more in bonds than personal loans.

a. Formulate an LP model for this problem with the objective of maximizing the expected return on the portfolio.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?