Question: A bank is attempting to determine where to invest its assets during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds, 6%; home loans, 8%; auto loans, 5%; personal loans, 10%. To ensure that the bank's portfolio is not too risky, the bank's investment manager has placed the following three restrictions on the bank's portfolio:

¦ The amount invested in personal loans cannot exceed the amount invested in bonds.

¦ The amount invested in home loans cannot exceed the amount invested in auto loans.

¦ No more than 25% of the total amount invested can be in personal loans. Help the bank maximize the annual return on its investment portfolio.