A person wants to invest an amount of ₹75,000. He has two options A and B yielding 8% and 9% return respectively on the invested amount. He plans to invest at least ₹15,000 in Plan A and at least ₹25,000 in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where x and y are investments Plan A and Plan B respectively?

maximize Z = 0.08x + 0.09y
x ≥ 15000
y ≥ 25000
x + y ≤ 75000
x ≤ y
x, y ≥ 0

The correct answer is Option (4).

Let $x$ be the investment in Plan A and $y$ be the investment in Plan B.

Total investment constraint

$x+y=75000$

Return to be maximized

$Z=0.08x+0.09y$

Given conditions

$x\ge15000$

$y\ge25000$

$x\le y$

The required LPP is:

Maximize $Z=0.08x+0.09y$

subject to

$x+y=75000,\;x\ge15000,\;y\ge25000,\;x\le y$