A retired person wants to invest an amount of Rs.50,000. His broker recommends investing in two types of bonds A and B yielding 10%

Points
Z=10100x+9100y
A(20000,10000) Z=Rs.2900
B(40000,10000) Rs.4900 (Maximize)
C(25000,25000) Rs.4750
D(20000,20000) Rs.3800
Let Rs.x invest in bond A and Rs.y invest in bond B.
Then A.T.P.
Maximize, z=10100x+9100y — (1)
Subject to constraints
x+y≤50,000 — (a)
x≥20,000 —(b)
y≥10,000 — (c)
and x≥y or x-y≥0 — (d)
and x≥0, y≥0
Now change inequality into equations
x+y=50,000, x=20,000, y=10,000, x=y
Region: put (0, 0) in (a), (b), (c), (d)
0≤50000 (towards origin)
0≥20,000 (away from origin)
0≥10,000 (away from origin)
As shown in the graph.
So from the tabular column, we conclude that he has to invest Rs.40,000 in 'A' and Rs.10,000 in bond 'B' to get maximum return Rs.4,900.