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Linear Programming is a technique used to help managers to make decisions regarding the production of products that involves limited resources. It is used to determine number of products to be produced that can maximize profit.
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Maximize: Z = 2X1 + 3X2
Objective function
Subject to: Courses of action
4X1 + 5X2 ≤ 6 7X1 + 8X2 ≤ 9 X1, X2 ≥ 0
Constraints
Objective function and constraints must be LINEAR
1.Identify the decision variables (products to be produced). 2.Identify the objective function (maximize profit / minimize cost). 3.Identify constraints (resources used to make products). 4.Identify the mathematical expressions for the constraints (amount of resources needed to make one product).
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A restaurant manager wants to determine number of plates of Meal A and Meal B to produce everyday. One plate of Meal A requires 20 minutes of ingredient preparation time while one plate of Meal B requires 40 minutes of ingredient preparation time. In addition, it takes 20 minutes to cook one plate of Meal A and 15 minutes to cook one plate of Meal B. Everyday, 10 hours of ingredient preparation time are available and 5 hours of cooking time are available. Meal A and Meal B can provide a profit of RM5 and RM8 for one plate respectively. Formulate a linear programming model for this problem.
Let X1 = Meal A, X2 = Meal B Maximize: Z = 5X1 + 8X2 Subject to: 20X1 + 40X2 ≤ 600 (ingredient preparation time) 20X1 + 15X2 ≤ 300 (cooking time) X1, X2 ≥ 0
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METHODS FOR SOLVING A LINEAR PROGRAMMING MODEL
Graphical Method
Simplex Method
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Can only be used when there are two variables in the model.
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Can be used when there are two or more than two variables in the model.
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The solution is made by using graph.
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The solution is made by using table.
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Steps: Draw graph. Identify the feasible region. Find the optimal solution.
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Involves repetitive process – need to do some calculations repeatedly until an optimal solution is reached.
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