Estimating the Number of Piano Tuners in Chicago

CASE DESCRIPTION:-

Have you heard of Piano tuners? Also called Piano technicians, these people make adjustments to the tension of a piano's strings, aligning the intervals between their tones so that the instrument is in tune, and provide repair & restoration services. Due to factors like temperature, humidity, and frequent use, every piano needs a tuner.

But why are we discussing tuners?

To solve a puzzle about piano tuners in Chicago! 

Your task is to assess the provided data to figure out how many piano tuners are needed for the population of Chicago using basic mathematics, logical reasoning, and your wits!!

Ready?

DATA:-

Chicago has 2 million households in the city that are (for the sake of simplicity) equally divided into 4 different income classes. The following table shows the % of each income class that owns a piano while calculating how many pianos it comes up to.

Considering how pricey a piano tuner’s services are ($150-200 per session!!), different income classes get it tuned at varying time differences. The Super-Rich folks do not care for such ‘chump change’ as they get it tuned once every year!

However, the Rich and the Middle-Class folks tend to be careful about their spending as the Rich families get it tuned once every 3 years while the Middle-Class people avail of a tuner’s services only once every 10 years!!

Every piano tuner can work on a total of 4 pianos every day for 300 days in a year (they have a life too). So how many tuners are needed?

[Hint: It’s not 175,000/4 = 43,750]

If 52 are registered on websites like Craigslist, is there an excess of piano tuners, or a shortage?? (Assume a registration rate of 65%)

ANALYSIS:-

Although 100,000 pianos are tuned every year, the remaining 75,000 are not. Thus, because not every piano is tuned every year, we need to determine the number of tuning requests that arise every year.

No. of Requests = (No. of pianos / time-gap of service)

Therefore, the sum total of this for all three income classes that have pianos will give us the final answer. Thus, the total tuning requests annually are:- 

(100,000/1 + 50,000/3 + 25,000/10) = 119,167.

For the sake of simplifying our calculations, let’s round it up to 120,000.

CONCLUSION:-

Therefore, the number of piano tuners needed to keep all of Chicago’s pianos tuned every year is:-

No. of tuners = (Annual tuning requirement/No. of days worked annually) / tuning capacity

                      = (120,000/300) / 4

                      = 400 / 4

                      = 100 tuners

Considering that only 52 are registered online, with a registration rate of 65%, the total number of tuners in Chicago are

                     = 52/65%

                     = 80

Thus, with an annual requirement of 100, there is a shortage of piano tuners in Chicago.

Was that difficult? 

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[Disclaimer: This case study is entirely hypothetical and unrelated to real-world situations. It's designed for educational purposes to illustrate theoretical concepts and potential scenarios within a given context. Any similarities to actual events or individuals are purely coincidental.]