7-Introduction to Linear Optimization

T 1c 2t 10 4c 3t 30 c t 0 big bricks small bricks the

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Unformatted text preview: ptimization (1940’s) •  Decisions: Number of Chairs and Tables to produce (C, T) •  Target: Maximize total proFit •  Constraints: –  Total available units of Big and Small bricks –  Non- negativity MAX 40*C + 50*T s.t. 1*C + 2*T ≤ 10 4*C + 3*T ≤ 30 C, T ≥ 0 (Big Bricks) (Small Bricks) The Lego Game - - Discussion •  Suppose now there are only 9 big bricks. •  What is the solution given by Excel solver? •  How are you going to deal with fractional solution? What is Optimization? Optimization refers to the selection of a best element from some set of best available alternatives. alternatives. Origin of Optimization (1940’s) •  George B. Dantzig (8 Nov 1914 – 13 May 2005) http://en.wikipedia.org/wiki/George_Dantzig Origin of Optimization roblem s) Dantzig’s Original P (1940’ •  Assigning 70 men to 70 jobs –  If solved with brutal force, how many alternatives are there? –  Suppose a computer (which can run 1 million computations per sec...
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