The management of Goham city needs to schedule workers to collect garbage every day. The worker capacity is measured in worker-hours. The demand for garbage collection has a normal distribution with a mean of 100 worker-hours and a standard deviation of 24 worker-hours.

If the number of worker-hours scheduled is more than the number of worker-hours required, the workers go home early but are paid $14 per hour for the total scheduled worker-hours. If the number of worker-hours scheduled is less than the number of worker-hours required, the workers have to do overtime and are paid at $21 per hour.

How many worker-hours should be scheduled each day to minimize costs? (Choose the option that is closest to the correct answer.)

A. 83
B. 90
C. 96
D. 106
E. 120
F. 130

To minimize costs, the management of Goham city needs to find the optimal number of worker-hours to schedule for garbage collection. The demand for garbage collection follows a normal distribution with a mean of 100 worker-hours and a standard deviation of 24 worker-hours.

The first step is to determine the cost implications of scheduling more worker-hours than required. In this case, if the number of worker-hours scheduled is more than the number of worker-hours required, the workers go home early but are still paid $14 per hour for the total scheduled worker-hours. This means that any excess worker-hours that are not utilized will still incur costs.

On the other hand, if the number of worker-hours scheduled is less than the number of worker-hours required, the workers will have to do overtime and will be paid at a higher rate of $21 per hour. This incurs additional costs due to the higher hourly rate.

To find the optimal scheduling that minimizes costs, we need to consider the trade-off between excess worker-hours and overtime. If we schedule too many worker-hours, we will have excess hours that are not utilized efficiently, leading to unnecessary costs. Conversely, if we schedule too few worker-hours, we will incur overtime costs.

By analyzing the given information, we can determine that the minimum cost will occur when the scheduled worker-hours are equal to the mean demand of 100 worker-hours. This ensures that the workers are neither sent home early nor required to work overtime. However, we should also consider the standard deviation in the demand for garbage collection. In order to have a buffer and accommodate any unforeseen fluctuations in demand, we can adjust the scheduled worker-hours accordingly.

Therefore, to minimize costs, the management of Goham city should schedule approximately 96 worker-hours each day. This provides a balance between meeting the average demand for garbage collection and accounting for potential variations in the actual demand.

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