A bank has $$650,000$ in assets to allocate among various investment options $$ bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of $10\%,$ mortgages $8\mathrm{.}5\%,$ car loans $9\mathrm{.}5\%,$ and personal loans $12\mathrm{.}5\%.$

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 at the minimum same amount is invested in mortgages as in personal loans. The bank also wants to invest more in bonds than personal loans. Formulate an LP model for this problem with the objective of maximizing the expected return on the portfolio. Implement your model in a spreadsheet and solve it$.$