Category Archives: General Mathematics

Real-Life Equipment Optimization Problem

I recently was asked to provide a recommendation on how to schedule the operating time for three different machines that were producing three different products. This is not a made up problem, but reflects a real production situation. My solution uses Excel's Solver and its linear programming-based optimization routine to find an optimal machine scheduling plan. The solution I provided has proven to be useful to the folks who asked for it, and I thought it was worth sharing my solution here. Continue reading

 
Posted in General Mathematics | 3 Comments

Daily Tree Consumption for Toilet Paper

I was reading an article on National Geographic when I spotted an interesting factoid about the impact of Toilet Paper (TP) world-wide tree consumption.

Toilet paper wipes out 27,000 trees a day.

Like many factoids, I doubt there is a way to actually measure this number – it can only be estimated. Thus, it is a prime candidate for a Fermi solution. Continue reading

 
Posted in General Mathematics, General Science | 4 Comments

Probability That An Old President Does Not Finish Their Term

Ronald Reagan (Figure 1) was our oldest president at the time of inauguration – 69 years 349 days old. The 2016 US presidential election is giving us a choice of two candidates that will be relatively old at inauguration: Donald Trump (70 years, 220 days), and Hilary Clinton (69 years, 86 days). Since US presidents often serve 2 terms, it is conceivable they we may have a 77- to 78-year old president in 2024. This fact makes me curious as to what is the likelihood that a 70 year-old's natural life will be long enough for them to serve one or two terms. Continue reading

 
Posted in General Mathematics, History Through Spreadsheets | Leave a comment

10,000 Boomers Turning 65 Everyday

The front-end of the baby boomers began to turn 65 in 2011 and they will continue to turn 65 until 2029. I started to wonder how many boomers are turning 65 every day? The Social Security Administration estimates that 10,000 Americans are turning 65 every day (source). As I thought about, I should be able to estimate the number of people that are turning 65 every day by examining graphs of the US population and birth rate (Figure 1). It is a nice Fermi problem and the subject of this post. Continue reading

 
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Nonlinear Piecewise Function for Stellar Luminosity vs Mass

A reader mentioned to me that the Wikipedia has an good article on stellar luminosity versus stellar mass– the article is a good one. I thought I would compare the empirical relationship shown in the Wikipedia with a couple of different data sets that I found on the web. I was motivated to perform this analysis because: (1) I have been doing some reading on exoplanets, and luminosity is important when it comes to exoplanet temperature; and (2) I am presenting a seminar on Mathcad to our engineering staff, and this application provides me a nice demonstration on how to compute nonlinear piecewise functions. Continue reading

 
Posted in Astronomy, General Mathematics | 1 Comment

Flattening the Golden Gate Bridge Deck

I recently read a post on Quora about the day that the arc of the Golden Gate Bridge was flattened by the load of a large number of people – some reports stated that as many as 300K people were present at the event. The bridge was opened opened to this huge throng of people as part of its golden anniversary. This was the first time I had heard of this event. Continue reading

 
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Decision Making Using the Analytic Hierarchy Process

I gave a seminar a few days ago on System Engineering – a favorite subject of mine. One of the topics covered during my System Engineering seminar was decision making. Specifically, I speak about how I want trade studies to be performed in my group. I have participated in hundreds of trade studies, and I have used many different approaches. Continue reading

 
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Mathcad Solution To XKCD Problem

XKCD is a great comic strip by Randall Munroe that takes a quirky look at the world of science. Randall recently posted a set of questions for a substitute teacher to pose to a math class that were interesting and attracted the attention of some problem-solving enthusiasts. Continue reading

 
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Propane Tank Math

I have used propane for years with my barbecue grill, but I have never used it for heating a space. While at university many decades ago, I worked in construction, and we used propane heaters to make working in partially-completed homes more comfortable in the winter. I went to Home Depot and purchased the propane heater shown in Figure 1. It is rated to put out 30K to 40K BTU/hr. This should provide enough heat to warm my garage so I can work in it comfortably. I like the fact that it is small, and I can easily store it during the summer. I have too much stuff to manage as it is, and I do not need any more big stuff. Continue reading

 
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Yet More Gift Wrapping

My sister and I talk about these practical math problems all the time. Here is another good video that covers gift wrapping with a mathematical slant. Continue reading

 
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