Modeling o Decision Variables:The decision variables completely describe the decisions to be made.Denote by x1 the number of soldiers produced each week,and by x2 the number of trains produced each week. o Objective Function:The function to be maximized or minimized is called the objective function.Since fixed costs (such as rent and insurance)do not depend on the values of x1 and x2,Giapetto can concentrate on maximizing his weekly profit,i.e.. max3x灯+2x2. ●Constraints: Each week,no more than 100 hours of finishing time may be used. Each week,no more than 80 hours of carpentry time may be used. Because of limited demand,at most 40 soldiers should be produced each week. 2x1+2≤100，为+9≤80，x1≤40. o Sign Restrictions:x为≥0andx2≥0. 0Q0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 6/41
Modeling Decision Variables: The decision variables completely describe the decisions to be made. Denote by x1 the number of soldiers produced each week, and by x2 the number of trains produced each week. Objective Function: The function to be maximized or minimized is called the objective function. Since fixed costs (such as rent and insurance) do not depend on the values of x1 and x2, Giapetto can concentrate on maximizing his weekly profit, i.e., max 3x1 + 2x2. Constraints: 1 Each week, no more than 100 hours of finishing time may be used. 2 Each week, no more than 80 hours of carpentry time may be used. 3 Because of limited demand, at most 40 soldiers should be produced each week. 2x1 + x2 ≤ 100, x1 + x2 ≤ 80, x1 ≤ 40. Sign Restrictions: x1 ≥ 0 and x2 ≥ 0. Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 6 / 41
Solution Approach General Procedure Modeling ③Solution Approach Linear Programming o Sensitivity Analysis Duality Theory o Commercial Softwares o Integer Programming Dynamic Programming o Game Theory OLTEX 4口，4得+4艺至，三风0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 7/41
Solution Approach 1 General Procedure 2 Modeling 3 Solution Approach Linear Programming Sensitivity Analysis Duality Theory Commercial Softwares Integer Programming Dynamic Programming Game Theory 4 LATEX Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 7 / 41
Solution Approach o Linear Programming (LP) o Integer Programming (IP) o Dynamic Programming(DP) ●Game Theory 4口，4得+4之，至三双0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 8/41
Solution Approach Linear Programming (LP) Integer Programming (IP) Dynamic Programming (DP) Game Theory Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 8 / 41
Solution Approach Linear Programming General Procedure Modeling ③Solution Approach ●Linear Programming o Sensitivity Analysis Duality Theory o Commercial Softwares o Integer Programming Dynamic Programming o Game Theory OLTEX 4口，4得+4艺至，三风0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 9/41
Solution Approach Linear Programming 1 General Procedure 2 Modeling 3 Solution Approach Linear Programming Sensitivity Analysis Duality Theory Commercial Softwares Integer Programming Dynamic Programming Game Theory 4 LATEX Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 9 / 41
Solution Approach Linear Programming oSimplex Method: The Big M Method The Two-Phase Simplex Method oSensitivity Analysis ●Duality 4口，4得+4之，至三风0 Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 10/41
Solution Approach Linear Programming Simplex Method: The Big M Method The Two-Phase Simplex Method Sensitivity Analysis Duality Xi Chen (chenxi0109@bfsu.edu.cn) Optimization Method 10 / 41