Answered Essay: Problem AWZ 73-923 a bank is attempting to determine where its assets should be invested

Problem AWZ 73-923 a bank is attempting to determine where its assets should be invested during the current year. At present, 1000,000 is available for investment in bonds, home loans, auto loans and personal loans. The annual rates of return on each type of investments are known to the following ; bonds 5%,home loans10%,auto loans 8%,personal loans15%. To ensure that the bank’s portfolio is not to risky, the bank’s investment manager has placed the following three 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 amout invested in auto loans . 3.- no more than 20% of the total amount invested can be in personal loans. help to maximize the annual return on its investmet portfolio. Formulate the decision question as a linear programming model, define the variables, write down the constrains and the objective function in mathematical terms ( variables, inequalities etc.)

explain please

Expert Answer

Decision variables:

Let B = Amount to be invested in bonds

H =Amount to be invested in home loans

A = Amount to be invested in auto loans

P = Amount to be invested in personal loans

Objective function:

Objective function is to maximize the returns

Z = Max 0.05B + 0.1H + 0.08A + 0.15P

s.t

B+H+A+P<= 1000000 (Maximum amount available. We can invest all the amount or less than available)

P <= B (or) P-B <=0 (The amount invested in personal loans cannot exceed the amount invested in bonds)

H<=A (or) H-A <= 0(the amount invested in home loans cannot exceed the amount invested in auto loans)

P<=0.2(B+H+A+P) (or) 0.8P – 0.2B-0.2H-0.2A (no more than 20% of the total amount invested can be in personal loans)

B, P, H, A >=0 (Non negativity constraint)

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