Question

Old hens can be brought at Rs 2 each and young ones at Rs 5 each. The old hens lay 3 eggs per week and the young ones lay 5 eggs per week, each egg being worth 30 paise. A hen cost Rs 1 per week to feed. Deepthi has only Rs 80 to spend for hens. How many hens of each kind should Deepthi buy to give a profit of more than Rs 6 per week assuming that Deepthi cannot house more than 20 hens. Solve graphically.

Answer 1

Max = 0.3 (3x + 5y) – (x + y)z 

= 0.5y – 0.1x 

subject to x + y ≤ 20 

2x + 5y ≤ 80 

0.1 + 0.5y ≥ 6 

x, y ≥ 0 

Plot the lines on the graph and Solution is z is max” at (0,16) & z_max = 8