L01_Formulation of LPPs

L01_Formulation of LPPs - AAOC C222 OPTIMISATION Text Book...

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AAOC C222: OPTIMISATION Text Book: Operations Research: An Introduction By Hamdy A.Taha (Pearson Education) 7 th Edition
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Reference Books: 1. Hadley, G: Linear Programming, Addison Wesley 2. Pant, J.C: Optimization, Jain Brothers
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3. Hillier & Lieberman Introduction to Operations Research, Tata McGraw-Hill 4. Bazaraa, Jarvis & Sherali Linear Programming and Network Flows, John Wiley
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http://discovery.bits- pilani.ac.in/discipline/math/msr/index. html You may view my lecture slides in the following site.
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The formal activities of Operations Research (OR) were initiated in England during World War II when a team of British scientists set out to make decisions regarding the best utilization of war material. Following the end of the war, the ideas advanced in military operations were adapted to improve efficiency and productivity in the civilian sector. Today, OR is a dominant and indispensable decision making tool.
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Example : The Burroughs garment company manufactures men's shirts and women’s blouses for Walmark Discount stores. Walmark will accept all the production supplied by Burroughs. The production process includes cutting, sewing and packaging. Burroughs employs 25 workers in the cutting department, 35 in the sewing department and 5 in the
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packaging department. The factory works one 8-hour shift, 5 days a week. The following table gives the time requirements and the profits per unit for the two garments:
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Garment Cutting Sewing Packaging Unit profit($) Shirts 20 70 12 8.00 Blouses 60 60 4 12.00 Minutes per unit Determine the optimal weekly production schedule for Burroughs.
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Solution: Assume that Burroughs produces x 1 shirts and x 2 blouses per week. 8 x 1 + 12 x 2 Time spent on cutting = Profit got = Time spent on sewing = 70 x 1 + 60 x 2 mts Time spent on packaging = 12 x 1 + 4 x 2 mts 20 x 1 + 60 x 2 mts
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The objective is to find x 1 , x 2 so as to maximize the profit z = 8 x 1 + 12 x 2 satisfying the constraints : 20 x 1 + 60 x 2 25 × 40 × 60 70 x 1 + 60 x 2 35 × 40 × 60 12 x 1 + 4 x 2 5 × 40 × 60 x 1 , x 2 ≥ 0, integers
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This is a typical optimization problem. Any
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This note was uploaded on 02/23/2011 for the course MATH 112 taught by Professor Ritadubey during the Spring '11 term at Amity University.

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L01_Formulation of LPPs - AAOC C222 OPTIMISATION Text Book...

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