PHPSimplex

Optimizing resources with Linear Programming



Fruit trees' problem

A farmer has a plot of land of 640m² to dedicate it to the cultivation of fruit trees: orange, pear, apple and lemon trees. He ask himself the way to distribute the surface of the land among the varieties to get the maximum benefit knowing that:

 

Determining decision variables and expressing them algebraically:

Determining the restrictions and expressing them as equations or inequalities in function of the decision variables. Such restrictions can be obteined from each land, work hours and water needs per tree:

Expressing all implicit conditions established by the origin of variables: negativeness, integer, only a few allowed values... . In this case, the restrictions are that the number of trees can't be negative and must be an integer number:

Determining objective function:

Solve with PHPSimplex.

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PHPSimplex
Version 0.81

Copyright ©2006-2016. All rights reserved.

Developed by:
Daniel Izquierdo Granja
Juan José Ruiz Ruiz

English translation by:
Luciano Miguel Tobaria

French translation by:
Ester Rute Ruiz