Question

The Top Investment Corporation is developing a mix of investments to meet the needs of a client with one million dollars to invest. A mix of five investments is being considered, with data on each as shown below: 

The state laws and Top Investment policies impose the following restrictions on the composition of the investments: . 

The total average return must be at least 12.5% where all the money must be invested.

Investments A and B together must not be over $700,000. 

Investment D may not exceed 20% of the total funds invested in all loans. 

a. Formulate an appropriate linear programming model that will maximize the total average annual return. 

b.The maximum amount to be invested in investment A, B, C, D and E are $345000, $275000, $250000, $125000 and $5000. What is the expected annual return for each investment and what is the annual rate of investment?

Answer 1

Part A. Formulating appropriate linear programming

Condition 1 - total average profit must be at least 12.5%.

10%A+12%B+16%C+14%D+9%E =>12.5%

Condition 2- investment in A and B must not exceed $700000

A + B =< $700000

Condition 3 - investment D may not exceed 20% of the total fund invested in all loan

D =< 20%(A+B+C+D+E)

therefore linear programming

• 10%A+12%B+16%C+14%D+9%E =>12.5%

• A+B =< $700000

• D =< 20%(A+B+C+D+E)

PART B. CALCULATION OF EXPECTED ANNUAL RATE OF RETURN

Fund	Investment	Rate of return	Actual return
A	345000	10%	34500
B	275000	12%	33000
C	250000	16%	40000
D	125000	14%	17500
E	5000	9%	450
Total			125450

Annual rate of return = actual reurre/total investment

Annual return = 125450/1000000×100 = 12.545%