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.

Question

Philoid · Accepted Answer

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

∴According to the question,

X + y

x , y

Maximize Z = 0.12x + 0.15y

The feasible region determined by X + y x ,

y 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 .