Question

Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they 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 year
Safeway	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 two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.

Formulate the LP model for this problem, using the standard LP format. Remember to define the objective function, the decision variables, and label the constraint functions. There is no need to solve the problem.

Answer 1

Decision Variables: Let the values of investment per month in each of the five investments: Fidelity, Optima, CaseWay, Safeway , National be a, b, c, d and e respectively.

Objective: To Maximize the Expected return of investment each month.

Return per Month = Investment per month * Interest rate/ Month

Objective Function:

Min(Return) = a * (9.1/12)/100 + b* (16.1/12)/100 + c*(7.3/12)/100 + d*(5.6/12)/100 + e*(12.3/12)/100

Min 1/1200 (9.1a + 16.1b + 7.3c + 5.6d + 12.3e) -----------> Objective Function

subject to constraints:

Maximum of 30% of total investment to be put in Optima and National:

b + e <= 0.3(a+b+c+d+e)

-0.3a + 0.7b -0.3c -0.3d + 0.7e <= 0    -----> 1st Constraint

Minimum of 40% of total investment to be made in Safeway and Fidelity:

a + d >= 0.4 (a+b+c+d+e)

0.6a -0.4b -0.4c +0.6d - 0.4e >= 0    -------> 2nd Constraint

a,b,c,d,e >= 0 (Non-Negative constraint to denote positive values of investment) -------> 3rd constraint