Linear Programming

# Linear Programming - L inear Programming I. In troduction...

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Linear Programming I. Introduction a. What? i. A mathematical (programming) technique for formulating and solving business problems ii. Optimization method- maximization of productivity and profit or minimizing cost of operations iii. Constant rate of return b. Development i. George B Dantzig in 1947 c. Three element of LP i. Objective function ii. Side constraints iii. Non-negativity conditions d. Example I: Kotna Company i. Maximize: Z=300x1+400x2 ii. Subject to: x1<=90 (truck department); x2<=60 (tractor department); 600/120 trucks=5, 600/100 tractors=6; 5x1+6x2<=600 (parts). And: x1, x2 >=0 iii. Where: x1 (number of trucks to be produced) and x2 (number of tractors to be produced), known as decision variables e. Solution Methods i. Graphic methods

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ii. Algebraic methods iii. Simplex methods iv. Computer applications 1. WinQSB=Window Quantitative Systems for Business a. Excel b. Lindo c. Lingo 2. Graphic Method a. Maximization problem b. Corner-point solutions: corner point 0, x1 0, x2 0, z
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## Linear Programming - L inear Programming I. In troduction...

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