Question

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 in personal loans. It also wants to invest more in bonds than personal loans.
Requried:
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 it the optimal solution?

Answer 1

Answer:

using solver, the optimal solution is:

$325,000 invested in bonds

$162,500.01 invested in mortgages

$162,499.99 invested in personal loans

maximum profit = $66,625

Explanation:

profit maximization equation:

0.1b + 0.085m + 0.095c + 0.125p

where:

b = money invested in bonds

m = money invested in mortgage loans

c = money invested in car loans

p = money invested in personal loans

constraints:

b + m + c + p ≤ 650,000

p ≤ 0.25 x 650,000 ⇒ p ≤ 162,500

m ˃ p

b ˃ p

using solver, the optimal solution is:

$325,000 invested in bonds

$162,500.01 invested in mortgages

$162,499.99 invested in personal loans

maximum profit = $66,625

actually solver gave me the following solution:

$325,000 invested in bonds

$162,500 invested in mortgages

$162,500 invested in personal loans

maximum profit = $66,625

since mortgage loans must be larger than personal loans, I added 1¢ to mortgage loans and subtracted 1¢ from personal loans