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# lecture_2 - Constraints IOE 310 Fall 2007 DECISION...

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A QUICK REVIEW OF MATERIAL YOU SHOULD KNOW IOE 310 Fall 2007

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INTRODUCTION TO LINEAR PROGRAMMING What is linear programming. Graphical solution of a linear programming problem. IOE 310 Fall 2007
AN EXAMPLE A manufacturer produces two toys Soldiers: sell at \$27 and require \$10 (raw mat), \$14 (labor). Trains: sell at \$21 and require \$9 (raw mat), \$10 (labor). Two types of scarce skilled labor is needed. Finishing. Hours available 100 Carpentry. Hours available 80 Finishing Carpentry Soldier 2 hours 1 hour Train 1 hour 1 hour Also, at most 40 soldiers can be sold each week. Formulate a model to maximize proﬁt. IOE 310 Fall 2007

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WHAT MAKES A LINEAR PROGRAM I Linear objective function. Linear constraints that are either equalities or inequalities. IOE 310 Fall 2007
FORMULATING A LINEAR PROGRAM I Decision Variables. Objective Function.

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Unformatted text preview: Constraints. IOE 310 Fall 2007 DECISION VARIABLES I x 1 the number of soldiers produced each week. x 2 the number of trains produced each week. IOE 310 Fall 2007 OBJECTIVE FUNCTION AND CONSTRAINTS I Express the proﬁt in terms of the decision variables. z = 3 x 1 + 2 x 2 Express the constraints in terms of the decision variables. 2 x 1 + x 2 ≤ 100 ‘Finishing’ x 1 + x 2 ≤ 80 ‘Carpentry’ x 1 ≤ 40 ‘limit’ x 1 ≥ x 2 ≥ IOE 310 Fall 2007 WHAT MAKES A LINEAR FUNCTION I proportionality. additivity. divisibility. certainty. IOE 310 Fall 2007 GRAPHICAL SOLUTION - DEFINITIONS I Feasible Region. Optimal solution. Corner Point Solution. Binding Constraints. Non-binding Constraints. IOE 310 Fall 2007 GRAPHICAL SOLUTION I IOE 310 Fall 2007...
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## This note was uploaded on 04/02/2008 for the course IOE 310 taught by Professor Saigal during the Spring '08 term at University of Michigan.

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lecture_2 - Constraints IOE 310 Fall 2007 DECISION...

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