Question

Old hens can be bought for Rs. 2 each. but young

ones cost Rs. 5 each. The old hens lay 3 eggs per
week and the young ones 5 eggs per week, each
egg being worth 30 paise. A hen costs Rs. 1.00 per
week to feed. If I have only Rs. 80.00 to spend for
hens, how many of each kind should I buy to give a
profit of more than Rs. 6.00 per week, assuming
that I can not house more than 20 hens.
Formulate this problem as LPP.

Answer 1

Let x be the number of old hens and y be the number of young hens to buy.

The objective is to maximize the profit, which is the total income from selling eggs minus the total cost of buying and feeding the hens:

Maximize Z = 0.3(3x + 5y) - (2x + 5y + (x + y)) - 6

where 0.3 is the price of each egg, 2 is the cost of an old hen, 5 is the cost of a young hen, and 1 is the cost of feeding a hen per week. The term "-6" is subtracted to ensure that the profit is more than Rs. 6.00 per week.

The constraints are:

The total cost of buying hens cannot exceed Rs. 80.00:

2x + 5y ≤ 80

The total number of hens cannot exceed 20:

x + y ≤ 20

The number of old hens cannot be negative:

x ≥ 0

The number of young hens cannot be negative:

y ≥ 0

Now we have formulated the problem as a linear programming problem. The objective is to maximize Z subject to the constraints.