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

The Correct Option is D

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).