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 \( x \) be the amount invested in plan A and \( y \) be the amount invested in plan B. The problem states:
1. The return rates for plan A and plan B are 9% and 10% respectively. Therefore, the total return function \( Z \) is: \[ Z = 0.09x + 0.1y \] This represents the total return from investments in both plans A and B.
2. The total investment should be at least ₹80,000, so the constraint is: \[ x + y \geq 80000 \]
3. The investment in plan A should not exceed investment in plan B, which gives the constraint: \[ x \leq y \]
4. The person wants to invest at least ₹20,000 in plan A and at least ₹30,000 in plan B, so the constraints are: \[ x \geq 20000 \quad \text{and} \quad y \geq 30000 \]
Thus, the Linear Programming Problem (LPP) model to maximize the return \( Z \) is: \[ \text{Maximize } Z = 0.09x + 0.1y \] Subject to the constraints: \[ x + y \geq 80000, \quad x \leq y, \quad x \geq 20000, \quad y \geq 30000 \] The correct answer is option (A).