MLF End Term: 28 April 2024 (January 2024 term)

A person went to the market to buy hens. Old hens can be bought for ₹ 200.00 each but young hens can be bought for ₹ 500.00 each. The old hens lay 3 eggs per week and the young hens lay 5 eggs per week. Each egg costs Rs. 11. A hen costs ₹ 50.00 per week to feed. If the financial constraint is ₹ 8000 per week to buy hens and the capacity constraint is that the total number of hens bought cannot exceed 20 per week. The objective is to earn more profit. Let x represent the number of old hens and y represent the number of young hens.
Use the above information to answer the given subquestions

Choose the correct Primal optimization problem from the following.

A person went to the market to buy hens. Old hens can be bought for ₹ 200.00 each but young hens can be bought for ₹ 500.00 each. The old hens lay 3 eggs per week and the young hens lay 5 eggs per week. Each egg costs Rs. 11. A hen costs ₹ 50.00 per week to feed. If the financial constraint is ₹ 8000 per week to buy hens and the capacity constraint is that the total number of hens bought cannot exceed 20 per week. The objective is to earn more profit. Let x represent the number of old hens and y represent the number of young hens.
Use the above information to answer the given subquestions

If (x*, y*) is the optimal solution of the primal, u1 and u2 are Lagrange multipliers then which of the following options is/are true?

A person went to the market to buy hens. Old hens can be bought for ₹ 200.00 each but young hens can be bought for ₹ 500.00 each. The old hens lay 3 eggs per week and the young hens lay 5 eggs per week. Each egg costs Rs. 11. A hen costs ₹ 50.00 per week to feed. If the financial constraint is ₹ 8000 per week to buy hens and the capacity constraint is that the total number of hens bought cannot exceed 20 per week. The objective is to earn more profit. Let x represent the number of old hens and y represent the number of young hens.
Use the above information to answer the given subquestions

Which of the following options is/are true?