Final answer:
The station is expected to not dispatch approximately 875 packages, arising from a shortfall in the Flex pool's capacity to deliver the remaining 8% of the day's volume after the DSPs have delivered their committed 92%.
Step-by-step explanation:
The student's question involves calculating the expected number of packages that will not be dispatched by a delivery station's Flex pool of drivers. The total volume of packages for the day is given as 57,544. The delivery service providers (DSPs) have committed to delivering 92% of these packages. This leaves 8% of the volume to be handled by the station's Flex pool. Furthermore, we know the station has a Flex pool of 150 drivers and a Standard Package Rate (SPR) of 25 packages per route.
To begin, calculate the number of packages the DSPs will handle: 57,544 x 0.92 = 52,940.32 packages. Next, identify the remaining volume for the Flex pool: 57,544 - 52,940.32 = 4,603.68 packages.
Then, divide the remaining volume by the SPR to find out how many routes are needed: 4,603.68 packages / 25 SPR = 184.1472 routes. Since we cannot have a fraction of a route, we round up to the nearest whole route, resulting in 185 routes needed for the Flex pool.
However, with only 150 drivers in the Flex pool, there will be packages that cannot be dispatched: 185 required routes - 150 available drivers = 35 routes short. Therefore, the number of undelivered packages we expect is 35 routes x 25 SPR = 875 packages.