Problem Solving Session 5.docx - Problem Solving Session 5...

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Problem Solving Session 5 Problem 1 Solve the problem algebraically (without using MS Excel) . 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 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 optimum objective function value. (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 Rangaswamy’s optimal production plan? How many acres of bananas should he produce if the profit drops below this level?

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