A bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans....

A bank is attempting to determine where its assets should be invested 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, 10%; home loans, 16%; auto loans, 13%; personal loans, 20%. 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.