#1 is correct.
#2 is wrong; the random arrival rate means that, in theory, all your customers could come right at the start of the day, at which point there’s a line. Therefore, the answer’s B.
#3 is wrong; A being the bottleneck means that the capacity of the process equals the capacity of A because you can’t go faster than your slowest process. As such, if we halve the rate of our slowest process, the capacity gets halved alongside it, so the answer is B.
#4 is correct with 75 minutes. B is the answer: 75 minutes is between 45 minutes and 1.5 hours.
#5 is fairly simple; x_1 + x_2
= 1 + 2
is less than 4 anyways, so it’s unaffected by this change, giving A as the answer. If it instead went down from 5 to 2, then it would cut into our objective solution - 1 + 2
is less than 4 but not less than 2, so our optimal solution would be affected - and decrease our optimal objective value.
#6 is wrong; utilization is the percentage of capacity that we’re using, so it’s equal to arrivals/service rate
. We’re keeping the number of arrivals the same, but we’re increasing our service rate, which gives us a lower utilization: we’re using a lower percentage of our service rate.