Question 2 A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres per hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society?Let the land allocated to Crop X be x hectare
and land allocated to crop Y be y hectare
According to Question :
Herbicide used for crop X = 20 litres per hectare
Herbicide used for crop Y = 10 litres per hectare
Maximum quantity of herbicide = 800 litres
∴ 20x + 10y ≤ 800
2x + y ≤ 800
Also,
Total land Available to grow crops = 50 hectare
∴ x + y ≤ 50
As we want to Maximize the Profit
Hence, the function used here is Maximize Z.
Profit from crop X = Rs 10500 per hectare
Profit from crop Y = Rs 9000 per hectare
Maximize Z = 10500 x + 9000 y
Combining all constraints :
Maximize Z = 10500 x + 9000 y
Subject to Constraints :
2x + y ≤ 80
x + y ≤ 50
x, y ≥ 0
Hence, the Profit will be maximum if :
Land Allocated to Crop X = 30 hectare
Land allocated to Crop Y = 20 hectare
Maximum Profit = Rs 4,95,000

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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