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

Hint:

When formulating a Linear Programming Problem (LPP), it’s essential to carefully define all the constraints that impact the decision variables. Each constraint reflects a real-world limitation or requirement that must be adhered to when solving the problem. In this case, we have constraints on individual investments, total investment, and the relationship between the investments in Plan A and Plan B. By accurately interpreting and translating these constraints into mathematical inequalities, you can form an effective LPP that ensures the investment strategy is optimal and feasible. Additionally, always ensure that the final solution respects these constraints for a practical solution.

Answer 1

The Correct Option is D

To optimize the return on investment for options A and B, a Linear Programming Problem (LPP) is formulated using the specified conditions. The decision variables are defined as:

• x: Investment amount in option A
• y: Investment amount in option B

The objective is to maximize the total returns, Z, expressed by the objective function:

Z=0.08x+0.09y

The problem is subject to the following constraints:

• x≥15000 (Minimum investment in option A)
• y≥25000 (Minimum investment in option B)
• x+y≤75000 (Maximum total investment)
• x≤y (Investment in option A cannot exceed investment in option B)
• x,y≥0(Non-negativity of investments)

The complete LPP formulation is:

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