Oom Lecture 01

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Everyday estimation problems:

• How many plumbers are there in Berkeley?

Population of Berkeley: ${\displaystyle few\cdot 10^{5}}$, breakable fixtures per person: few, fixture breakage rate: 1 per 10 years, so the demand is ${\displaystyle few\cdot 10^{4}}$ fixtures per year. If a year is 250 work days, and a plumber can fix 3 fixtures per workday, then it takes 50 plumbers to meet the demand of Berkeley. The yellow pages has 200 listings.

• How much lipstick has Brittany Spears eaten?

Substitute chapstick for lipstick. Then think in bulk: Eugene uses 1 stick every 2 months. Then take data: chapstick is 5 grams. Brittany Spears is 25 and has probably been using lipstick for 15 years. So at 30 grams per year, for 15 years, this is about 1 lb. of worn lipstick. How much of this did she eat? Eugene says the efficiency factor is O(1). So BS has probably eaten 0.5 lbs.

• Amount of money in an armored car?

The natural length scale of the problem is that of a human, so we’ll say this car is 6x6x12 ft. A bill is (performing a measurement) 5x3 inches. What about thickness? Thinking in bulk: a 500 page book is about 2 inches. This comes to ${\displaystyle 1\cdot 10^{7}}$ bills in a truck. If these are 20’s, we have ${\displaystyle 2\cdot 10^{8}}$ dollars. At 1g per bill, this comes to 10 metric tons, and that’s a little full. We’ll say you can only fill a truck to 3, which means there are 70 million dollars in a full armored car.