Introduction 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. oObjective 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: 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≥0andx2≥0. Xi Chen (chenxi0109@bfsu.edu.cn) Linear Programming 4/148Introduction 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) Linear Programming 4 / 148