Question

Daniel needs to assign his mechanics to four pending jobs. The table below shows how much time (in minutes) it takes each mechanic to perform each job. Help Daniel determine the optimal assignments. 4 Worker A B с D Job (Time in Minutes) 2 5 9 3 8 5 5 4 3 5 4 8 5 7 4 4 5 In the optimal solution, who should be assigned to work on Job 4? O Worker Worker A Worker B Worker D

Answer 1

Answer: Option 1: Worker C

Explanation:

Excel LP formation (Assignment Problem)

K L M N U Р R 1 1 2 3 4 2 Worker /Job 3 A Objective Function Min 5 9 5 7 0 4 B 3 8 4 4 5 с 5 5 8 4 6 D 7 4 5 5 7 8 Worker /Job 9 A 1 2 3 4 Total 0 1 10 B 0 1 11 с 0 1 12 D 0 1 13 Total 0 0 0 0 14 = 15 1 1 1 1 16

Formula:

K L M N O Q R 1 1 2 3 2 Worker/Job 3 4 7 Objective Function =SUMPRODUCT(L3:06, 19:012) A 5 9 5 Min 4 B 3 8 4 4 5 С 5 8 4 6 D 7 4 5 5 7 8 Worker /Job 9 1 12 3 4 A B 10 Total =SUM(L9:09) =SUM(L10:010) =SUM(L11:011) =SUM(L12:012) 1 11 С 1 12 D Total 13 =SUM(L9:L12) =SUM(M9:M12) =SUM(N9:N12) =SUM(09:012) 14 15 1 1

Solver Parameters:

Solver Parameters Set Objective: SOS3 To: o Max Min O Value of: 0 By Changing Variable Cells: SL59:505121 Subject to the Constraints: $L$9:$0$12 = binary SLS13:$0$13 = $L$15:$0$15 SP$9:$PS12 = $R$9:$R$12 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Solution:

K L M N 0 P R 1 3 2 Worker /Job 3 A 4 B 2 9 8 4 7 Objective Function Min 5 5 3 16 4 4 с 5 8 4 5 6 5 7 D 4 Ол 5 7 8 Worker /Job 9 A 1 3 4 2 0 Total 1 0 1 0 1 10 B 1 0 0 0 1 1 11 C 0 0 0 1 1 1 12 D 0 1 0 0 1 1 13 Total 1 1 1 1 14 II II 15 1 1 1 1