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 exceedthe 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 rate of return on each type of investment is known to be: 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:
a. The amount invested in personal loans cannot exceed the amount invested in bonds.
b. The amount invested in home loans cannot exceed the amount invested in auto loans.
c. No more than 25% of the total amount invested may be in personal loans.
The bank’s objective is to maximize the annual return on its investment portfolio. Formulate an LP that will enable the bank to meet this goal.
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