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%; and 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.
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
of return
the following: bonds, 10%; home loans, 16%; auto
loans, 13%; and 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.
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