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.


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 .


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