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Consider a farmer owning 45 acres of land. The farmer is going to plant his/her land with wheat or corn. Each acre planted with wheat yields $200 profit; each with corn yields $300 profit. Resource usage for each acre planted with wheat/corn are given in the table below. Wheat Corn Available Resource Labor 3 Workers 2 Workers 100 Workers Fertilizer 2 tons 4 tons 120 tons The model for the problem is given below. Max z = 200x1 + 300x2 s.t.

Consider a farmer owning 45 acres of land. The farmer is going to plant his/her land with wheat or corn. Each acre planted with wheat yields $200 profit; each with corn yields $300 profit. Resource usage for each acre planted with wheat/corn are given in the table below. Wheat Corn Available Resource Labor 3 Workers 2 Workers 100 Workers Fertilizer 2 tons 4 tons 120 tons The model for the problem is given below. Max z = 200x1 + 300x2 s.t.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 74P
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Consider a farmer owning 45 acres of land. The farmer is going to plant his/her land with wheat or corn. Each acre planted with wheat yields $200 profit; each with corn yields $300 profit. Resource usage for each acre planted with wheat/corn are given in the table below. Wheat Corn Available Resource Labor 3 Workers 2 Workers 100 Workers Fertilizer 2 tons 4 tons 120 tons The model for the problem is given below. Μaxz 200x, + 300x2 s.t. Зх, + 2х, < 100 2х, + 4x, < 120 X1 + x2 < 45 X1, X2 2 0 а. Find a range for the profit of wheat in which current optimal basis remains optimal. b. Find a range for the profit of corn in which current optimal basis remains optimal. Find a range for the available workers in which current optimal basis remains optimal. d. Find a range for the available fertilizer in which current optimal basis remains optimal. С. е. Find a range for the available land in which current optimal basis remains optimal.
Transcribed Image Text:Consider a farmer owning 45 acres of land. The farmer is going to plant his/her land with wheat or corn. Each acre planted with wheat yields $200 profit; each with corn yields $300 profit. Resource usage for each acre planted with wheat/corn are given in the table below. Wheat Corn Available Resource Labor 3 Workers 2 Workers 100 Workers Fertilizer 2 tons 4 tons 120 tons The model for the problem is given below. Μaxz 200x, + 300x2 s.t. Зх, + 2х, < 100 2х, + 4x, < 120 X1 + x2 < 45 X1, X2 2 0 а. Find a range for the profit of wheat in which current optimal basis remains optimal. b. Find a range for the profit of corn in which current optimal basis remains optimal. Find a range for the available workers in which current optimal basis remains optimal. d. Find a range for the available fertilizer in which current optimal basis remains optimal. С. е. Find a range for the available land in which current optimal basis remains optimal.
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