BU275 Lecture Notes - Lecture 1: Microbrewery, Feasible Region, Linear Programming

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8 Jan 2017
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A small keg of lager (20l) takes 5 kg of malted barely and 0. 06kg of hops (~2 ounces) and sells for . A small keg of ale (20l) takes 2kg of barley and 0. 12 kg of hops, sells for . We only have 50 kg of barley today and 0. 84kg of hops. Constrained resources: give rise to a resource table: In general, 5x1 + 2x2, barley is limited so 5x1 + 5x2< 50 constraint 1: hops required: 0. 06x1 + 0. 12x2, but hops is limited too so 0. 06x1 + 0. 12x2< 0. 84 constraint 2. Constraints: x1>= 0 constraint 3, x2>=0 constraint 4. Linear programs can be solved graphically, one axis per decision variable. One way to graph our constraints is to rewrite them as lines: 0. 06x1 + 0. 12 x2 <= 0. 84 becomes 0. 06x+0. 12y=0. 84. A feasible solution satisfies all the constraints. The feasible region is the set of all feasible solutions.

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