A bank is attempting to determine where its assets should be invested during the current year. At present $1,000,000 is available for investments in bonds,home loan,auto loans, and personal loans. The annual rates of return of each type o investment are known to be the following bonds, 5%; home loans, 8%; auto loans,10%, personal loans 15%. to ensure that the bank's portfolio is not to risky, the bank's investment manager was placed the following 3 restrictions on the bank's portfolio: 1.- The amount invested in personal loans cannot exceed the amount invested in bonds. 2.- the amount invested in home loans cannot exceed the amount invested in auto loans. 3.- No more than 20% of the total amount invested can be in personal loans. Help the bank to maximize the annual return on its investment portfolio,
Decision Variables: B, HL, AL, PL = amount invest in bonds, home loans, auto loans and personal loans respectively. Objective: Max 0.05B + 0.08HL + 0.1AL + 0.15PL s.t. XB + HL + AL + PL <= 1000000, PL - B <= 0, HL - AL <= 0, -.02B - 0.2HL - 0.2AL + 0.8PL <= 0.