There are 5 different machines in the workshop. It costs 1000 euros to teach a worker to operate any one of the machines. For what minimal cost can 8 workers be instructed to operate machines so that all the machines can operate simultaneously even if any 3 of the workers are absent? Each worker can operate only one machine at a time.
2007-06-21 06:06:58 · 3 answers · asked by oregfiu 7 in Science & Mathematics ➔ Mathematics
The minimal cost is 20000 euros !
Every machine must be learned by 4 workers, because if not the 3 workers are less that know the machine can be ill or absent. So 5x4=20 is the minimal cost in educations. This is also sufficient because
W1 : M1 M4 M5
W2 : M1 M4
W3 : M1 M3 M5
W4 : M1 M3
W5 : M2 M3 M5
W6 : M2 M3
W7 : M2 M4 M5
W8 : M2 M4,
is a possible configuration that always works !
2007-06-21 06:46:21 · answer #1 · answered by ?????? 7 · 2⤊ 0⤋
There are 5 machines, and at a minimum 4 workers must be trained for each machine. So that's 20 training sessions at 1000 apiece, which adds up to 20000 euros.
2007-06-21 13:35:26 · answer #2 · answered by John G 2 · 1⤊ 0⤋
2000
2007-06-21 13:11:26 · answer #3 · answered by Anonymous · 0⤊ 2⤋