4120-lecture3 - Computational Methods for Management and...

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Unformatted text preview: Computational Methods for Management and Economics Carla Gomes Lecture 3 Reading: 3.1- 3.3 of textbook Outline of Lecture • Linear Programming: – Wyndor Example: • Problem Formulation • Graphical Solution • Linear Programming Terminology • Sensitivity Analysis Wyndor Glass Co. Product Mix Problem • Wyndor has developed the following new products: – An 8-foot glass door with aluminum framing. – A 4-foot by 6-foot double-hung, wood-framed window. • The company has three plants – Plant 1 produces aluminum frames and hardware. – Plant 2 produces wood frames. – Plant 3 produces glass and assembles the windows and doors. Questions: 1. Should they go ahead with launching these two new products? 2. If so, what should be the product mix ? Algebraic Model for Wyndor Glass Co. Let D = door production rate (in batches) W = window production rate (in batches) Maximize P = 3 D + 5 W subject to D ≤ 4 2 W ≤ 12 3 D + 2 W ≤ 18 and D ≥ 0, W ≥ 0. A graphical solution 1. Graph the line associated with each of the linear inequality constraints. 2. Determine on which side of each of these lines the feasible region must lie. Since this problem is two dimensional it is possible to provide a graphical solution. To graphically find the feasible region, we will follow these steps: Graphing the Product Mix P r o d u c t i o n r a t e ( u n i t s p e r w e e k ) f o r w i n d o w s A product mix of A product mix of 1 2 3 4 5 6 7 8-1-1-2 1 2 3 4 5 6 7 8-2 P r o d u c t i o n r a t e ( u n i t s p e r w e e k ) f o r w i n d o w s Production rate (units per week) for doors (4, 6) (2, 3) D = 4 and W = 6 D = 2 and W = 3 Origin D W Graph Showing Non-Negativity Constraints: D ≥ 0 and W ≥ 0 P r o d u c t i o n r a t e f o r w i n d o w s 8 6 4 2 2 4 6 8 Production rate for doors P r o d u c t i o n r a t e f o r w i n d o w s D W Nonnegative Solutions Permitted by D ≤ 4 P r o d u c t i o n r a t e f o r w i n d o w s D W 8 6 4 2 2 4 6 8 Production rate for doors P r o d u c t i o n r a t e f o r w i n d o w s D = 4 Nonnegative Solutions Permitted by 2 W ≤ 12 Production rate for doors 8 6 4 2 2 4 6 8 2 W = 12 D W Production rate for windows Boundary Line for Constraint...
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This note was uploaded on 02/25/2011 for the course AEM 4120 taught by Professor Gomes,c. during the Fall '08 term at Cornell University (Engineering School).

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4120-lecture3 - Computational Methods for Management and...

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