personal loans $14\mathrm{.}5\%.$ To make sure the portfolio is not too risky, the bank wants to restrict persona

invested in mortgages as is invested in personal loans. The bank also wants to invest at least as mu

mortgages, car loans, and personal loans, respectively.$)$

$($a$)$ Formulate an LP model for this problem with the objective of maximizing the expected return

MAX:

$0\mathrm{.}12x_1+0\mathrm{.}105x_2+0\mathrm{.}115x_3+0\mathrm{.}145x_4$

Subject to:

total amount spent

$x_1+x_2+x_3+x_4=628000$

amount for personal loans

$x_{4}0\mathrm{.}25*628000$

mortgages and personal loans

$x_2{x}_4$

bonds and personal loans

bonds and personal loans $x_1{x}_4$

$x_1,x_2,x_3,x_{4}0$

$($b$)$ Implement your model in a spreadsheet and solve it$.$ What is the optimal solution?