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 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. How much money should be allocated to each type of loan to maximize the return in interest?

Make sure to give the algebraic equations and inequalities.

a) Define the decision variables

b) Write the objective function

c) Write the set of constraints.