Chap_02 - Business Decision Making and Management Science...

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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 1 Chapter 2 Linear Programming: Model Formulation and Graphical Solution Business Decision Making and Management Science
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 2 Chapter Topics Model Formulation A Maximization Model Example Graphical Solutions of Linear Programming Models A Minimization Model Example Irregular Types of Linear Programming Models Characteristics of Linear Programming Problems
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 3 Decision variables - mathematical symbols representing levels of activity of a firm. Objective function - a linear mathematical relationship describing an objective of the firm, in terms of decision variables, that is maximized or minimized Constraints - restrictions placed on the firm by the operating environment stated in linear relationships of the decision variables. Parameters - numerical coefficients and constants used in the objective function and constraint equations. Model Components and Formulation
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 4 Resource Requirements Product Labor (hr/unit) Clay (lb/unit) Profit ($/unit) Bowl 1 4 40 Mug 2 3 50 Problem Definition A Maximization Model Example (1 of 2) Product mix problem - Beaver Creek Pottery Company How many bowls and mugs should be produced to maximize profits given labor and materials constraints? Product resource requirements and unit profit:
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 5 Problem Definition A Maximization Model Example (2 of 3) Resource 40 hrs of labor per day Availability: 120 lbs of clay Decision x 1 = number of bowls to produce per day Variables: x 2 = number of mugs to produce per day Objective Maximize Z = $40x 1 + $50x 2 Function: Where Z = profit per day Resource 1x 1 + 2x 2 40 hours of labor Constraints: 4x 1 + 3x 2 120 pounds of clay Non-Negativity x 1 0; x 2 0 Constraints:
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 6 Problem Definition A Maximization Model Example (3 of 3) Complete Linear Programming Model: Maximize Z = $40x 1 + $50x 2 subject to: 1x 1 + 2x 2 40 4x 2 + 3x 2 120 x 1 , x 2 0
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 7 A feasible solution does not violate any of the constraints: Example x 1 = 5 bowls x 2 = 10 mugs Z = $40x 1 + $50x 2 = $700 Labor constraint check: 1(5) + 2(10) = 25 < 40 hours, within constraint Clay constraint check: 4(5) + 3(10) = 70 < 120 pounds, within constraint Feasible Solutions
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Chapter 2 - Linear Programming: Model Formulation and Graphical Solution 8 An infeasible solution violates at least one of the
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