Rangaswamy owns 50 acres of land in the Hassan district of Karnataka on which he grows bananas and papayas. The total cost of producing bananas is Rs. 1,05,000 per acre while the total cost for papayas is Rs. 2,10,000 per acre. For the coming year Rangaswamy has a budget of Rs. 63,00,000. He does not want to use any more than 15 acres for bananas and plans on using at least 20 acres for papayas. The profit from each acre of bananas is Rs. 80,000 and from papayas is Rs. 1,40,000. a) Formulate a linear programming problem (call this Primal LPP) to help Rangaswamy decide how many acres of each fruit to produce in order to maximize his total profit. Clearly define all the decision variables, objective function and constraints.
Rangaswamy owns 50 acres of land in the Hassan district of Karnataka on which he grows bananas and papayas. The total cost of producing bananas is Rs. 1,05,000 per acre while the total cost for papayas is Rs. 2,10,000 per acre. For the coming year Rangaswamy has a budget of Rs. 63,00,000. He does not want to use any more than 15 acres for bananas and plans on using at least 20 acres for papayas. The profit from each acre of bananas is Rs. 80,000 and from papayas is Rs. 1,40,000. a) Formulate a linear programming problem (call this Primal LPP) to help Rangaswamy decide how many acres of each fruit to produce in order to maximize his total profit. Clearly define all the decision variables, objective function and constraints.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 1
Rangaswamy owns 50 acres of land in the Hassan district of Karnataka on which he grows
bananas and papayas. The total cost of producing bananas is Rs. 1,05,000 per acre while the
total cost for papayas is Rs. 2,10,000 per acre. For the coming year Rangaswamy has a budget
of Rs. 63,00,000. He does not want to use any more than 15 acres for bananas and plans on
using at least 20 acres for papayas. The profit from each acre of bananas is Rs. 80,000 and from
papayas is Rs. 1,40,000.
a) Formulate a linear programming problem (call this Primal LPP) to help Rangaswamy
decide how many acres of each fruit to produce in order to maximize his total profit.
Clearly define all the decision variables, objective function and constraints.
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