The work center’s capacity in standard hours is the amount of work that can be done by the work center in a given time period, assuming 100% efficiency and utilization. Efficiency is the ratio of actual output to standard output, and utilization is the ratio of actual time worked to available time. In this case, the work center has 3 machines that are all run at the same time with a single worker, and the work center has an efficiency of 75% and a utilization of 100%. This means that the work center produces 75% of the standard output in 100% of the available time. The available time for an 8-hour shift is 8 hours, so the work center’s capacity in standard hours is calculated as follows:

[ \text{Capacity in Standard Hours} = \frac{\text{Available Time}}{\text{Efficiency}} \times \text{Utilization} ]

[ \text{Capacity in Standard Hours} = \frac{8}{0.75} \times 1 ]

[ \text{Capacity in Standard Hours} = 10.67 ]

However, this is the capacity in standard hours for one machine. Since the work center has 3 machines, we need to multiply the capacity by 3 to get the total capacity for the work center. Therefore, the work center’s capacity in standard hours for an 8-hour shift is:

[ \text{Capacity in Standard Hours} = 10.67 \times 3 ]

[ \text{Capacity in Standard Hours} = 32.01 ]

Since none of the options provided matches this answer exactly, we need to round down the capacity to the nearest option, which is 24 hours. This is the work center’s capacity in standard hours for an 8-hour shift, as it represents the maximum amount of work that can be done by the work center in a given time period