A man plan to start a polutry farm by investing at most rs.3000 .he can buy an old hens for rs.80 each and young one for rs.180 each but he cann't house more than 30 hens .old hen lay 4 eggs per week and young one lay 5 eggs per week , each egg sold at rs.5 . it cost rs.5 to feed an old hen and rs.8 to feed a young hen per week. formulate this problem determining the number of hen of each type he should buy so as to earn a profit of more than rs.300 per week
Answers
Answer:
We solve this problem by turning the question into two equations. (When the question was set in ancient China they were not able to do this since this technique had not yet been invented. And perhaps this is why there are, in fact, four solutions.)
If the number of cocks, hens and chicks are x, y and z. Then we have
(A) x + y + z = 100
(B) 5x + 3y + z/3 = 100
Given : A man plan to start a polutry farm by investing at most rs.3000 .he can buy an old hens for rs.80 each and young one for rs.180 each but he cann't house more than 30 hens .old hen lay 4 eggs per week and young one lay 5 eggs per week , each egg sold at rs.5 . it cost rs.5 to feed an old hen and rs.8 to feed a young hen per week
To Find : formulate this problem for maximum profit
Solution:
Old Hen = X
Young Hen = Y
80 X + 180Y ≤ 3000
=> 4X + 9Y ≤ 150
X + Y ≤ 30
Profit
= 5 * 4X - 5X + 5 * 5Y - 8Y
= 15X + 17Y
4X + 9Y ≤ 150
X + Y ≤ 30
points are ( 0 , 16.66) , ( 24 , 6) , ( 30 , 0)
Profit maximum at
(24 , 6) = 24 * 15 + 6 * 17
= 360 + 102
= 462 Rs
24 old hen & 6 young hen will give maximum profit
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