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# lecture1 - CS 435 Linear Optimization Fall 2008 Lecture 1...

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Unformatted text preview: CS 435 : Linear Optimization Fall 2008 Lecture 1: Introduction Lecturer: Sundar Vishwanathan Computer Science & Engineering Indian Institute of Technology, Bombay This subject rst came up for study in the manufacturing and industrial engineering areas in the 1940s. We begin with an example. A factory needs to produce n di erent goods from m di erent kinds of raw materials. Each good, in the process of its manufacture, uses a certain proportion of each available raw material. The amount of each raw material available is limited. Each good manufactured yields a certain amount of pro t. The problem is to determine how much quantity of each good to produce using these raw materials in order to maximize the total pro t on the goods. We will allow fractional amounts of goods to be produced. You are given: Raw Materials Available: M 1 , M 2 , M 3 , ¡ ¡ ¡ , M m Quantity of each material available: b 1 , b 2 , b 3 , ¡ ¡ ¡ , b m Goods to be produced: G 1 , G 2 , G 3 , ¡ ¡ ¡ , G n Pro t per unit of each good:...
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lecture1 - CS 435 Linear Optimization Fall 2008 Lecture 1...

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