Question

Anil wants to invest at the most ₹12000 in bonds A and B. According to rules, he has to invest at least ₹2000 in bond A and at least ₹4000 in bond B. if the rate of interest of bond A is 8% per annum and on bond B, it is 10% per annum, how should he invest his money for maximum interest? Solve the problem graphically.

Answer 1

Let the invested money in bond A be x and in bond B be y.

∴According to the question,

X + y ≤ 12000, x ≥ 2000, y ≥ 4000

Maximize Z = 0.08x + 0.10y

The feasible region determined by X + y ≤ 12000, x ≥ 2000, y ≥ 4000 is given by

The corner points of the feasible region are A(2000,4000) , B(2000,10000) and C(8000,4000) . 

The value of Z at the corner point are

Corner Point	Z = 0.08x + 0.10y
A(2000, 4000)	560
B(2000, 10000)	1160	Maximum
C(8000, 4000)	1040

The maximum value of Z is 116770 at point (2000,10000)

So, he must invest Rs.2000 in bond A and Rs.10000 in bond B.

The maximum annual income is Rs.1160 .