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. 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? f) Does Rangaswamy stand to make a higher profit if he relaxes the maximum limit of 15 acres he plans on using for producing bananas? Why or why not? If yes, what would he gain per additional acre that he allows for producing bananas? How many additional acres will this additional gain per acre be valid for?
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. 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? f) Does Rangaswamy stand to make a higher profit if he relaxes the maximum limit of 15 acres he plans on using for producing bananas? Why or why not? If yes, what would he gain per additional acre that he allows for producing bananas? How many additional acres will this additional gain per acre be valid for?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
100%
Please do (f)
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.
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?
f) Does Rangaswamy stand to make a higher profit if he relaxes the maximum limit of
15 acres he plans on using for producing bananas? Why or why not? If yes, what
would he gain per additional acre that he allows for producing bananas? How many
additional acres will this additional gain per acre be valid for?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 9 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.