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b) Use the graphical method to find the optimal solution and optimal objective function value. Use the graph paper provided and show all work on the graph. c) How many acres of land should Rangaswamy plan on cultivating in the coming year? d) It is expected that the profit per acre from bananas will drop in the coming year due to over-production of bananas in other regions. To what level can the profit per acre from bananas drop without affecting Ramaswamy's optimal production plan? How many acres of bananas should be produced if the profit drops below this level? e) Due to a shortage of papayas, the profit will increase to Rs. 1,60,000 per acre. What are the various production plans that will maximize Ramaswamy's total profit?

b) Use the graphical method to find the optimal solution and optimal objective function value. Use the graph paper provided and show all work on the graph. c) How many acres of land should Rangaswamy plan on cultivating in the coming year? d) It is expected that the profit per acre from bananas will drop in the coming year due to over-production of bananas in other regions. To what level can the profit per acre from bananas drop without affecting Ramaswamy's optimal production plan? How many acres of bananas should be produced if the profit drops below this level? e) Due to a shortage of papayas, the profit will increase to Rs. 1,60,000 per acre. What are the various production plans that will maximize Ramaswamy's total profit?

Advanced Engineering Mathematics
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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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. b) Use the graphical method to find the optimal solution and optimal objective function value. Use the graph paper provided and show all work on the graph. c) How many acres of land should Rangaswamy plan on cultivating in the coming year? d) It is expected that the profit per acre from bananas will drop in the coming year due to over-production of bananas in other regions. To what level can the profit per acre from bananas drop without affecting Ramaswamy's optimal production plan? How many acres of bananas should be produced if the profit drops below this level? e) Due to a shortage of papayas, the profit will increase to Rs. 1,60,000 per acre. What are the various production plans that will maximize Ramaswamy's total profit?
Transcribed Image Text: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. b) Use the graphical method to find the optimal solution and optimal objective function value. Use the graph paper provided and show all work on the graph. c) How many acres of land should Rangaswamy plan on cultivating in the coming year? d) It is expected that the profit per acre from bananas will drop in the coming year due to over-production of bananas in other regions. To what level can the profit per acre from bananas drop without affecting Ramaswamy's optimal production plan? How many acres of bananas should be produced if the profit drops below this level? e) Due to a shortage of papayas, the profit will increase to Rs. 1,60,000 per acre. What are the various production plans that will maximize Ramaswamy's total profit?
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