Final Answer:
The minimum number of compartments in the utility boxes must be 23 (Option 3). To accommodate all months, considering February's 28 days and accounting for leap years, a minimum of 24 compartments is required. Thus, Option 3, with 23 compartments, falls short of this necessity.
Step-by-step explanation:
The utility boxes must meet the minimum requirement to have at least one compartment for each day of the month. Since there are 31 days in the longest month, the minimum number of compartments needed is 31. However, the question provides answer choices up to 24 compartments. To determine the correct answer within the given choices, consider the months with fewer days. The shortest month, February, has 28 days. Therefore, the utility box must have at least 28 compartments to accommodate the days of February. However, adding one more compartment ensures coverage for all months, making it 29 compartments. To be safe for leap years, it's advisable to have at least 30 compartments. Considering the provided options, 23 compartments fall short of the necessary capacity, and 24 compartments meet the minimum requirement for all months, making 23 the correct answer.
In summary, by considering the months with the fewest days and accounting for potential leap years, the utility box must have a minimum of 24 compartments to cover all scenarios. Therefore, the correct answer to the question is 23 (Option 3).