A retired person wants to invest an amount of upto ₹20000. His broker recommends investing in two types of bonds A and B, bond A yielding 8% return on the amount invested and bond B yielding 7% return on the amount invested. After some consideration, he decides to invest atleast ₹5000 in bond A and no more than ₹8000 in bond B. He also wants to invest atleast as much in bond A as in bond B. Formulate as L.P.P. to maximize his return on investments.

Maximize $Z=0.08x+0.07y$
Subject to:
$x+y≤20000$
$x≥5000$
$y≤8000$
$x≥y$
$x,y≥0$

The correct answer is Option (2) → Maximize $Z=0.08x+0.07y$ Subject to: $x+y≤20000,x≥5000,y≤8000,x≥y,x,y≥0$

Let the person invest ₹x in bonds of type A and ₹y in bonds of type B, then his earning i.e. return (in ₹)

$Z = 8\%\, of\, x + 7\%\, of\, y = 0.08x + 0.07y$.

As the person can invest upto ₹20000, so investment constraint is

$x + y ≤20000$.

Other investment constraints are

$x ≥ 5000, y ≤ 8000, x ≥y$.

Non-negativity constraints are $x ≥0, y≥0$.

Thus, mathematically formulation of the L.P.P. is

Maximize $Z = 0.08x +0.07y$ subject to the constraints

$x + y ≤20000, x ≥ 5000, y ≤ 8000, x≥y, x ≥0, y ≥0$.