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Introduc_1

# Introduc_1 - Operations Research Text Book Operations...

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Operations Research Text Book: Operations Research: An Introduction By Hamdy A.Taha (Pearson Education) 8 th Edition

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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.
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 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.
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
This is a typical optimization problem. Any values of x 1 , x 2 that satisfy all the constraints of the model is called a feasible solution . We are interested in finding the optimum feasible solution that gives the maximum profit while satisfying all the constraints.

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More generally, an optimization problem looks as follows: Determine the decision variables x 1 , x 2 , …, x n so as to optimize an objective function f ( x 1 , x 2 , …, x n ) satisfying the constraints g i ( x 1 , x 2 , …, x n ) ≤ b i (i=1, 2, …, m).
Linear Programming Problems(LPP ) An optimization

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