Question

Mr. Dass wants to invest ₹12000 in public provident fund (PPF) and in national bonds. He has to invest at least ₹1000 in PPF and at least ₹2000 in bonds. If the rate of interest on PPF is 12% per annum and that on bonds is 15% per annum, how should he invest the money to earn maximum annual income? Also find the maximum annual income.

Answer 1

Let the invested money in PPF be x and in national bonds be y.

∴According to the question, 

X + y ≤ 12000

x ≥ 1000, y ≥ 2000  

Maximize Z = 0.12x + 0.15y 

The feasible region determined by X + y ≤ 12000, x ≥ 1000, 

y ≥ 2000 is given by

The corner points of the feasible region are A(1000,11000) , B(1000,2000) and C(10000,2000) . 

The value of Z at the corner point are

The maximum value of Z is 1770 at point A(1000,11000). 

So, he must invest Rs.1000 in PPF and Rs.11000 in national bonds. 

The maximum annual income is Rs.1770 .