What is the minimum unit production time:

What is the optimal value of X_A1 :

What is the optimal value of X_C2 :

What is the optimal value of X_D3 :

What is the optimal value of X_D2 :

There are four employees and three machines in a job-shop and production manager wants to assign the employees to the machines to minimize the production time per unit. The timetable below shows the number of minutes spent by each employee on each machine: Machine 1 D Employee 2 3 A 8 18 17 B 11 15 20 12 19 14 13 12 25 You see below a linear programming model that assigns each employee to only one machine, which ensures the minimum unit production time. Note: While solving the model in the program, you should specify by yourselves the correct sign "SIGN" (e.g. 5, S, 2), and right hand side "RHS" value for each constraint. Z: Unit Production time Xij = 1 if employee i is assigned to j, 0 otherwise where i = (A, B, C, D) j= (1, 2, 3) Min Z = 8XA1 + 18XA2 + 17XA3 + 11XB1 + 15XB2 + 20XB3 + 12Xc1 + 19XC2 + 14XC3 + 13XD1 + 12XD2 + 25XD3 s.t. XA1 + XA2 + XA3 "SIGN" "RHS" XA1 + XB1 + Xci +XD1 "SIGN" "RHS" XB1 + XB2 + XB3 "SIGN" "RHS" XA2 + XB2 + XC2 + XD2 "SIGN" "RHS" Xc1 + Xc2 + XC3 "SIGN" "RHS" XA3 + XB3 + Xc3 + XD3 "SIGN" "RHS" XD1 + XD2 + XD3 "SIGN" "RHS" Xij = 0 or 1 for all i, j