A popular smoothie bar, BlendItUp, can prepare a maximum of 80 smoothies per hour. On a busy Saturday afternoon, the bar actually prepares 60 smoothies per hour, but the manager wants to keep some spare capacity to handle unexpected rushes. Based on this information, what is the utilization of the smoothie bar during that period, and what is the capacity cushion it effectively maintains?

Question

BlackTom AI · Accepted Answer

First, restating the scenario helps frame the calculation: the smoothie bar can produce a maximum of 80 smoothies per hour, but during the busy period it actually produces 60 per hour, and we’re asked for utilization and capacity cushion.
Option A: Utilization = 60%, Capacity Cushion = 40%. This would imply that 60% of max capacity is being used and 40% spare capacity. However, 60 out of 80 is 75%, not 60%, so this option misstates both the utilization and the cushion.
Option B: Utilization = 40%, Capacity Cushion = 60%. Here the numbers suggest only 40% usage with 60% spare. Since actual output (60) is higher than 40% of max (32), this is inconsistent with the given 60 smoothies per hour, making this option incorrect.
Option C: Utilization = 25%, Capacity Cushion = 75%. This would mean a very low usage of the facility, with only a quarter of capacity used. But 60 out of 80 corresponds to 75% utilization, so this option is inaccurate.
Option D: Utilization = 75%, Capacity Cushion = 25%. This matches the arithmetic: utilization is actual output divided by max capacity, 60/80 = 0.75, i.e., 75%. The capacity cushion is the leftover capacity relative to max, which is (max − actual) / max = (80 − 60) / 80 = 20/80 = 0.25, i.e., 25%.
Thus, the correct pair is 75% utilization and a 25% capacity cushion, aligning with the provided numbers and definitions.

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