Question

A person wants to invest 75,000 in options A and B, which yield returns of 8% and 9% respectively. He plans to invest at least 15,000 in Plan A, 25,000 in Plan B, and keep Plan A ≤ Plan B. Formulate the LPP to maximize the return.

• A. maximize Z=0.08x+0.09y,
  x≥15000,
  y≥25000,
  x+y≤75000,
  x≤y, x,y≥0
• B. maximize Z=0.08x+0.09y,
  x≥15000,
  y≥25000,
  x+y≤75000,
  x≥y, x,y≥0
• C. maximize Z=0.08x+0.09y,
  x≥15000,
  y≥25000,
  x+y≤75000,
  x≥y, x,y≥0
• D. maximize Z=0.08x+0.09y,
  x≥15000,
  y≥25000,
  x+y≤75000,
  x≤y, x,y≥0

Answer 1

Answer: (D)

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

Answer 2

The Linear Programming Problem (LPP) for maximizing the return must satisfy the given constraints:

$x \geq 15,000$: At least Rs.15,000 is invested in Plan A.

$y \geq 25,000$: At least Rs.25,000 is invested in Plan B.

$x + y \leq 75,000$: The total investment does not exceed Rs.75,000.

$x \leq y$: The investment in Plan A does not exceed the investment in Plan B.

$x, y \geq 0$: Investments cannot be negative.

Thus, the correct representation of the LPP is option (4).