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 $8\mathrm{.}5\%,$ 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 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