dolution

Determine the optimal crop area using linear programming model to maximize the farmer’s net profit. A farmer has 150 ha farm. He grows Tomatoes, Potatoes and Brinjal in his farm. The price obtained is Rs. 10 per kg of Tomatoes, Rs 25 per kg of Potatoes and Rs. 7.50 per kg of Brinjal. The average yield per ha is 5 tonnes of Tomatoes, 10 tonnes of potatoes and 2 tonnes of Brinjal. The fertilizer is available to him at the cost of Rs. 5 per kg and the quantity is 20 tonnes. Each ha of Tomato requires 150 kg, potatoes requires 90 kg/ha and Brinjal requires 200 kg/ha of fertilizer. The labour requirement is 50 man days for Tomatoes, 85 man days for potatoes and 60 man days for Brinjal for every ha of crop. Total Man days available to the farmer are 800 and cost of labour is Rs. 400 per Man day.