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In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost.However, there are constraints like the budget, number of workers, production capacity, space, etc.In these lessons, we will learn about linear programming and how to use linear programming to solve word problems.
The following videos gives examples of linear programming problems and how to test the vertices.
The Graphical Method (graphic solving) is an excellent alternative for the representation and solving of Linear Programming models that have two decision variables.
Formulate and solve graphically a Linear Programming model for this problem.
Clearly outline the domain of feasible solutions and the process used to find the optimal solution and the optimal value.
Linear programming deals with this type of problems using inequalities and graphical solution method. She must buy at least 5 oranges and the number of oranges must be less than twice the number of peaches.
An orange weighs 150 grams and a peach weighs 100 grams.Given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control.The first product described has a market value (sale price) of US.0 per unit.Choose the scales so that the feasible region is shown fully within the grid.(if necessary, draft it out on a graph paper first.) Shade out all the unwanted regions and label the required region It also possible to test the vertices of the feasible region to find the minimum or maximum values, instead of using the linear objective function.Decision Variables: The first constraint represents the daily assembly time constraints.The second constraint is the availability of time for quality control (also daily).For the graphical solution of this model we will use the Graphic Linear Optimizer (GLP) software. The optimal solution is and with an optimal value that represents the workshop’s profit.Exercise #2: A winemaking company has recently acquired a 110 hectares piece of land.For this purpose there are computational tools that assist in applying the graphical model, like TORA, IORTutorial and Geogebra.Within this context we will present a series of Linear Programming exercises that have been solved using the graphical method.