Different Breakeven Points

I am in Puerto Rico, attending a conference.  As part of pre-conference events, I took a tour of the radio telescope at Arecibo. 

About 50 of us boarded a charted bus and traveled about 1.5 hours to the site.  Along the way, I listened in to a conversation in which two people discussed breakeven points of conferences and other events.

As they discussed this topic, my brain sort of went Dah! because any event has to breakeven before making a profit.

This is something my students can relate to because when they become juniors and seniors, their class takes over running the concession stand at school.  They have to stock the concession stand with sodas, chips, and other snacks.  To do this, they usually get a copy of the Span Alaska catalogue, prepare an order, send it off before waiting several weeks for the supplies to arrive.

Although they use the money in their class account to purchase the supplies, I don't think their advisor has ever taken time to explain how to calculate profit.  Just think, the breakeven point for this is when they've earned the money to cover their original expenditure.  A part of the original expenditure includes the shipping to get it all out to the village.  To make this more relevant, I plan to have students calculate the amount of profit they will make by determining the amount of money they could make if they sell everything at certain prices.

If I take this idea a step further, I could have students figure out the cost of everything for the prom, including food, entertainment, and supplies.  Then they have to decide how many people need to attend to breakeven based on the price of tickets.  Then they need to look at projections of possible profit based on the number of people attending based on price. 

Students at my school tend to charge the same as in the others in the past.  I do not believe students look at the price of tickets to project attendance so they know what they should charge for maximum profit.  Most times, class advisors do not have students do any type of projections.  The standard way is to order the supplies and sell without any calculations or thought.

In other areas, students could use different types of events such as dances to do the same types of calculation.  If we tie breakeven to events students are more familiar with, maybe they will understand the concept better since these are situations they relate to or have prior knowledge.

Monday, I'll be off to another topic.  I hope you all have a wonderful day.  Take care and let me know what you think.

Break Even Points

I got to wondering about cost per units, breakeven points, and profit.  This takes things one step further than just figuring out cost per unit of objects when shopping.

The reality is: we do teach these as linear equations in general but we provide the formulas and we ask the questions.  We seldom let them explore equations to find the information themselves. 

I do not believe most of my students have a good understanding of breakeven points or of the equation itself.  They can identify the parts but I think they can do the math without really understanding the topic.

I plan to create a short unit where I have students research the cost of purchasing a game app.  There are several websites where a person can purchase the script for a game with the understanding they will make a few changes so they are not simply reselling the original game.  This is part of the startup cost.  Next they have to figure out how much they want to sell the new app for so they can find the rest of equation so they can calculate the number of units they need to sell to find breakeven point. 

Once they have the breakeven point, I will throw in the idea they do not get all of the money every time an app is sold.  I want to introduce they pay a percentage to apple store or google store for them to handle all purchases so the return they actually get is less than what they charge so that might change the cost per unit and change the breakeven point.

This is important because my students have no knowledge of how a person decides the unit cost especially when looking at a product such as a game app for mobile devices.  My students think they get to keep every bit of money the app is sold for.  In addition the start up cost means very little to students out in the Bush of Alaska because most people who start a business do so in an old abandoned building or use part of a room.  They don't see any of that as part of the start up cost.

Once the students have the new equation and breakeven point, I want to throw in the idea of having to add more games because most games have a length of interest before people want to move on to another game.  I honestly believe this will make the idea of cost, revenue, and breakeven more relevant and understandable.  Let me know what you think.

Mercury and Apollo Space Crafts.

  I just attended a conference in Phoenix which was strong on science.  One of the things I attended, included information on various space craft and a bit on the actual astronauts.

As you know the first astronauts were actually rather small in they could not be over 5 foot 11 and could weigh no more than 180 lbs due to the size of the Mercury Capsule.

The capsule was only 6 ft 10 in tall and 6 ft 2.5 inches in diameter.  I think it would be great to have students calculate the amount of volume in a cylinder of that size.  I realize the capsule is not a cylinder but using a cylinder makes it easier.  It gives an idea of the space an astronaut lived in for several days.  It would not be that hard to have students create a cylinder out of construction paper or cardboard to provide a visual representation to give students a better idea of size.

Apollo 11 was a lot bigger at 10 ft 7 in by 12 ft 10 inches but it had three people instead of only one in the Mercury.  Again, it is easy to have students calculate the volume but they could take it a step further to determine if the amount of space per person is the same or smaller?  If it is less per person, they can calculate the percent difference with space per person.

If you want to take it further, look at the International Space Section which is 356 feet by 240 feet.  What is the volume  of this craft which houses up to 10 people at any one time.  How many square feet are allowed per person and how does it compare to the mercury capsule? 

I realize that the volume calculated for each space craft includes electronics, seats and other objects but I want to have students calculate volume, and space per person before having them brain storm on why just calculating volume per person can be slightly misleading.  I want them to do research to see if they can find the information on the amount of space planned for the astronauts. 

I am off to load.  I am on my way to Puerto Rico and will be arriving there a bit later today.  Have a good day.

July 4th

Cost of Travel.

  I am currently in Phoenix as I write today's entry.  When I purchased my tickets, I had to decide which routing I wanted.  If you do enough travel, you know you usually have so many different choices on routing and cost.

What factors do people look at when deciding on selecting the ticket.  Some routes, you really don't have much choice because there are only two or three flights a day, while other routes have tons of choices.

In addition, you often have to look at arrival times.  I travel to a place where the last flight arrives at midnight but the car rental places shut down by 9 PM.  So I end up renting a hotel room for the night, pick up the car the next morning and I'm off.

I usually look for the cheapest routing but tonight I wondered if the cheapest ticket is actually the cheapest?  Can we look at just the total cost or can we look at the cost based on the price per mile? Should one include the cost of the hotel room as part of the cost?

I travel with an airline who offers more perks with each level gained.  When you get to 20,000 miles, you earn the status of MVP or Most Valued Passenger.  I usually get this level due to living in Alaska.  Every time I fly to Seattle, I get between 1500 and 2000 miles depending on the routing.  At 40,000 miles, you become MVP Gold and if you manage 75,000 miles you become a MVP Platinum.  I've never gotten that high but I have managed MVP Gold a couple of years.  Gold gives you some First Class upgrades you can use on purchased tickets but you are also bumped up to First Class if there is space.

So you may wonder where I am going with this?  If the cheapest really the cheapest or if you paid a bit more and got 500 miles more is that better.  Being the geek I am, I've been known to sit down and calculate the cost per mile to see which one was actually a better price.   I also look at the additional cost of the miles if I pay for a longer routing. 

Later this summer, I am traveling to Finland but I have to fly from Alaska to DC before I head off to Finland.  I have to do this because there are two flights out of Anchorage each week but the days do not work for getting back to work on August 14th so I had to look at alternatives.  The cost was not much more going that routing and I get a bunch more miles on my frequent flyer account.

I want my students plan a trip, choose their flights, and provide their reasons for selecting said routing.  I also want them to calculate the cost per mile to see if there is much of a difference between choices.

Let me know what you think.  Have a great day and a wonderful 4th of July celebration. Be back on Wednesday with more math.  

Warm-up

Warm-up