Question

A person wants to invest at least ₹20,000 in plan A and ₹30,000 in plan B. The return rates are 9% and 10% respectively. He wants the total investment to be ₹80,000 and investment in A should not exceed investment in B. Which of the following is the correct LPP model (maximize return $ Z $)?

• A. Maximize \( Z = 0.09x + 0.1y \)
• B. Maximize \( Z = 0.1x + 0.09y \)
• C. Maximize \( Z = 0.15x + 0.10y \)
• D. Maximize \( Z = 0.10x + 0.09y \)

Hint:

In LPP, the objective function represents the goal of the problem (maximizing profit, return, etc.), and the constraints represent the limitations or conditions that need to be satisfied.

Answer 1

The Correct Option is A

Let \( x \) represent the amount invested in plan A and \( y \) represent the amount invested in plan B.The problem is formulated as follows:
1. Plan A yields a 9% return and plan B yields a 10% return. The total return function \( Z \) is therefore:\[Z = 0.09x + 0.1y\]
2. The total investment must be at least ₹80,000, leading to the constraint:\[x + y \geq 80000\]3. Investment in plan A cannot exceed investment in plan B:\[x \leq y\]4. Minimum investments are ₹20,000 for plan A and ₹30,000 for plan B:\[x \geq 20000 \quad \text{and} \quad y \geq 30000\]The Linear Programming Problem (LPP) to maximize return \( Z \) is:\[\text{Maximize } Z = 0.09x + 0.1y\]Subject to:\[x + y \geq 80000, \quad x \leq y, \quad x \geq 20000, \quad y \geq 30000\]Option (A) is the correct answer.