Question

You want to invest 40.000 TL at the beginning of each year for the next 5 years. You have got following options: If you deposit your money in the bank, you get 5% interest income per year. Also, if you invest your money in a 3-year municipal-bond, you can get 6.5% per year and have a current market price equal to 104% of face value. However, the government deducts 12% tax per year from the interest income you get from the bank. How should your investment be planned ?

(create only the lp model dont solve the problem)

Answer 1

Let X be the amount to be invested in the bank and

1.04Y (being the current market price)be the amount to be invested in the municipal bond.(Face value assumed to be1/-)

Objective function:

income from bank (after deduction of tax): 5 (1-0.12) = 4.4% = 0.044 X per annum for a period of 5 years.

income from government: 6.5%= 0.065 Y per annum for a period of 3 years.

Our objective will be maximise income :

Maximise Z = 0.044X + 0.065Y

Constraints:

1. The maximum amount can be invested in both the alternatives is 40.000 TL so,

X + 1.04Y < 40.000

FINALLY THE SOLUTION WILL BE AS FOLLOWS:

Maxmise objective function Max Z = 0.044X + 0.065 Y

subject to constraints:

X + 1.04 Y < 40.000 ------(being amount availability constraint)

   X ,Y > 0 --------------------( being non negativity constraint)