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Unformatted text preview: U. of Illinois MATH 482 Lecture 8 In class exercises The goal of this worksheet is to introduce to you the concepts and motivations of the theory of duality in linear programming. This is the topic of chapter 3 of the textbook 1. Consider the following resource allocation problem: UIUCbucks makes three kinds of coffee drinks (UIU-cap, Illin-ice coffee and the 482) which uses their very special (trademark) coffee beans and very special local, organic milk. They do so well with it, that they just make a bunch and sell it to stores, rather than dealing with the hassle of opening a caf e themselves. (a) Write down an LP that describes how much of each drink they should make in order to maximize profit subject to the fact that they only have b beans and b milk worth of coffee and milk. (You may use the variables x UIU cap etc to represent the amount of UIU-cap made, and the constant c UIU cap to represent the amount of profit made per UIU- cap sold. Also, let a beans,UIU cap be the amount of beans needed to make one unit of UIU-cap....
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- Spring '08
- Linear Programming