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Unformatted text preview: IEOR 162, Fall 2011 Suggested Solution to Homework 03 Problem 1 (Problem 3.Review.1) Let x 1 = barrels of beer produced and x 2 = barrels of ale produced. Then the problem can be formulated as z * = max 5 x 1 + 2 x 2 s.t. 5 x 1 + 2 x 2 ≤ 60 (Total amount of corns) 2 x 1 + x 2 ≤ 25 (Total amount of hops) x 1 ≥ x 2 ≥ . The graphical solution of this problem is shown in Figure 1. The feasible region is the shaded zone. The dotted line is the isoprofit line with (5 , 2) as the improving direction. Since the isoprofit line is parallel to the line 5 x 1 + 2 x 2 = 60, any point on 5 x 1 + 2 x 2 = 60 between the two points A = (10 , 5) and B = (12 , 0) is an optimal solution. For example, (10 , 5), (11 , 2 . 5), and (12 , 0) are all optimal solutions. All these points gives us the maximized objective value z * = 60. Therefore, Bloomington Breweries may produce 10 barrels of beer and 5 barrels of ale and receive $60 as its revenue. This is just one of the optimal solutions....
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 Fall '07
 Zhang
 Optimization, Cjt xjt

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