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: BlendItUp can produce up to 80 smoothies per hour, but during the busy period it makes 60 per hour, while still keeping some spare capacity. We need to compute two metrics: utilization and capacity cushion.
Option 1: Utilization = 40%, Capacity Cushion = 60%. This would imply actual output is 40% of max, i.e., 0.40 × 80 = 32 smoothies per hour, which does not match the given actual 60. Therefore this option is incorrect.
Option 2: Utilization = 25%, Capacity Cushion = 75%. A utilization of 25% corresponds to 0.25 × 80 = 20 smoothies per hour, far from the stated 60, so this option is not valid given the data.
Option 3: Utilization = 75%, Capacity Cushion = 25%. Here, 75% utilization means 0.75 × 80 = 60 smoothies per hour, which aligns exactly with the actual production. The capacity cushion of 25% equals (80 − 60) / 80 = 20 / 80 = 0.25, or 25%, representing the leftover capacity to handle extra demand.
Option 4: Utilization = 60%, Capacity Cushion = 40%. A 60% utilization would imply 0.60 × 80 = 48 smoothies per hour, not matching the reported 60. Moreover, the cushion would be (80 − 48) / 80 = 32 / 80 = 40%, which contradicts the stated 40% cushion given the actual figure. This combination is inconsistent with the data provided.
In summary, the only option that coherently matches an actual throughput of 60 smoothies per hour with the maximum capacity of 80 is the 75% utilization and 25% capacity cushion scenario, since 60 equals 0.75 × 80 and the remaining spare capacity is 20 smoothies per hour, i.e., 25% of max capacity.

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