The Museum's Attendance Problem
The city museum has seen a 20% decline in visitors over the past year, from 100,000 to 80,000. The director proposes extending opening hours from 5 PM to 9 PM on weekdays, believing this will attract working professionals. The museum's annual budget is $2 million, and extending hours would cost an additional $300,000 per year in staff and utilities. A survey of 1,000 city residents found that 60% work until 6 PM or later, and 40% of those said they would visit the museum if it were open later. The museum currently has no evening programs and relies on ticket sales for 30% of its revenue. The average ticket price is $10.
1. What is the maximum additional annual revenue the museum would need to generate from extended hours to justify the $300,000 cost, assuming ticket sales are the only new revenue?
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The museum needs additional revenue of at least $300,000 to cover the added cost. At $10 per ticket, that requires 30,000 additional visits per year. However, the museum must also consider whether the survey's 40% of 60% (i.e., 24% of residents) who say they would visit translates into actual visits. With a city population of unknown size, but survey of 1,000, the potential is 240 people from the survey, but that's a sample. The key is that the museum needs 30,000 additional visits, which is 37.5% of the current 80,000 visitors. The survey suggests 24% of residents might visit, but without knowing the total population, we cannot directly compute. The reasoning shows that the required increase is substantial and may not be met by the survey's indicated interest.
2. What assumption is necessary for the director's proposal to be valid?
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The director assumes that the working professionals who say they would visit will actually do so and that they are not already visiting at other times. Also, the director assumes that the additional revenue from ticket sales will at least cover the $300,000 cost. The survey indicates interest, but stated interest does not always translate into action. Furthermore, the museum must assume that the extended hours will not cannibalize existing attendance (i.e., people who currently visit during the day will switch to evening, not increasing total visits). Without these assumptions, the proposal may not be financially viable.