Question

ximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selectedthey do not change their mind. The investment plans offered are:

Fidelity                  9.1% return per year

Optima            16.1% return per year CaseWay         7.3% return per yearSafeway 5.6% return per year

National           12.3% return per year

Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these twoinvestments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in theseinvestments.

Formulate the LP model for this problem.

Answer 1

Solution

Since the amount of total investment is not specified, we take it to be S......................................................................... (1)

Let x₁, x₂, x₃, x₄, x₅ be the amount invested in Fidelity, Optima, CaseWay, Safeway and National respectively……….....…..(2)

Then, total annual return would be: 0.091x₁ + 0.161x₂ + 0.073x₃ +0.056x₄ + 0.123x₅ …..................................................…. (3)

Since the Sweets want to maximize this return, the objective function would be:

Maximize z = 0.091x₁ + 0.161x₂ + 0.073x₃ +0.056x₄ + 0.123x₅ ……………………….......................................................…. (4)

Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. => x₂ + x₅≤ 0.3S [vide (1) and (2)].................................................................................................... (5)

Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments. =>

x₄ + x₁≥ 0.4S [vide (1) and (2)]............................................................................................................................................... (6)

(5) and (6) form the constraints.

Thus, the LP formulation of the given problem is:

Maximize z = 0.091x₁+ 0.161x₂+ 0.073x₃+0.056x₄+ 0.123x₅

Subject to

x₂ + x₅≤ 0.3S

x₄ + x₁≥ 0.4S

x₁, x₂, x₃, x₄, x₅ ≥ 0.

Answer