Apathetic Thursday

The first person to complete this test with 100% or more will win an “i 8 Pi” shirt. Answers may be submitted via email to mathnerd@apatheticthursday.net.

Use the information below to answer the following questions. Show your work for full credit.

JK Diecut cuts rubber golf cart mats. Pallets of rubber are shipped in, each pallet containing 8 rolls of rubber. Each roll is 37 inches wide and needs to be cut into 20 sections each measuring 45 1/2 inches long. Each section produces 3 golf cart mats. Cut mats are placed in boxes, each box holding 60 mats. 9 Boxes are placed on a pallet to be shipped out.

If JK Diecut receives 15 pallets of rubber to cut, how many sections need to be cut?

How many mats will be produced?

How many pallets will be shipped out?

If it takes six punches of the die press to cut a section into mats, how many punches will it take to complete the order?

If it takes 5 minutes to cut a roll into sections and 15 minutes to cut a box of mats, how long does it take to complete a pallet?

How long will the whole order take?

Bonus Question 1: Say it only takes 3 minutes to cut a roll into sections and 12 minutes to cut a box of mats. How long will a pallet take now? How about the whole order?

If there are 3 people working this job at all times, how many man hours will the job take?

Each mat is worth $1.30. How much is each pallet worth?

If JK diecut requires 65% of the order to go back to the business for expenses, what is the highest hourly wage they can offer to their employees for this job?

Bonus Question 2: If the employees can work as fast as stated in Bonus Question 1, what is the highest hourly wage that can be offered the the employees?

It use to take 45 minutes to cut a roll and 30 minutes to cut a box. How long would this order have taken then?

Bonus Question 3: If the employees work at the old speed, what is the highest hourly wage that they can be offered?

How much longer did the old method take?

In the past it took 3 punches of the die press to cut a mat. How many punches would this order have taken?

Each saw cut shaves 1/8 an inch off the roll. How much rubber is wasted per roll on this step? How much for the whole order?

Given the shape and dimension of the mat below, give the area of the mat and calculate the rubber wasted from each section when it is cut into mats.

Add the wasted product from the saw cuts to the rubber wasted from each section.

Bonus Question 4: The saw runs for 3 seconds to cut each section. If the saw speed is 5400 rpm and acceleration and deceleration are practically instantaneous, how many revolutions does the saw blade make for the full order?

JK Diecut has a dumpster named Eliot. The Managers want to know how many times Eliot will need to be emptied over the course of the order. Eliot’s base measures 56 inches by 25 inches while Eliot’s top measures 64 inches by 32 inches. Eliot is 42 inches tall.

Assume the following:
- The rubber is placed into Eliot carefully and efficiently, leaving only 10% of the dumpster space unused. (Due to holes and air pockets.)
- The 10% of free dumpster space may be filled will the rubber shavings from the saw cuts.
-The garbage company refuses to pick up the dumpster if the lid does not fully close. (The dumpster may not be filled past the top.)
- The rubber that is being cut is all 3/16 inches thick.

How many times will the dumpster need to be emptied during the course of the order?

In ideal situations each roll should have enough rubber for 20 sections. In reality some only have enough rubber for 19 sections. It is estimated that 23% of the rolls only produce 19 sections, rather than 20. How does this effect the number of outgoing boxes?

How does this affect the total order cost?

How about the employee’s wage?

Bonus Question 5: The Rubber Manufacturer hears JK Diecut’s estimates and decided to check out things out for themselves. They find that in 240 rolls 17% are under 913 inches long, the minimum length needed to produce 20 sections. In Their test they find that the average length is 918.85 inches with a standard deviation of 14.66 inches. Assume that the distribution of roll length is approximately normal with mean u. Is there evidence that u is less than 913 inches?

Bonus Question 6: State the null and alternative hypotheses and choose a significance level. Then calculate the test statistic and find the P-Value. Is this significant?

xkcd

dive into mark

Although, I have to say, there isn’t much point to any of those fields, if you can’t communicate your findings/theories/knowledge to a future generation… (But I’m not good enough to do a comic of that…)

(EDIT: actually entered the photos, both for better user experience and a test with some other things I am working on.)

I am a math guy, and I enjoy doing math. So I like Pi, I think it’s a very interesting and amazing number, however, I also really like pie. For me, Pi Day is about celebrating the Greek Letter Pi, but also about baking pie.

Check back later today for today’s pie baking adventure.

I am an information parasite. I thrive on information. I sit and absorb as much info as my curious little ears can take in. It’s not all relevant. It’s not all useful. This doesn’t matter though, it’s information and thats what I need.  I don’t always even remember the info I take in, but the important part was that for an instant, if only an instant, I had that knowledge.

I came to this conclusion today while walking back to my dorm room. Last semester I finished up my math minor, but I had not taken Linear Algebra yet. If I took Linear Algebra this semester I would have to pay extra because I would be in “credit overload” with 20 or 21 credits. It would also give me a lot of homework to work on. Going into this semester I saw that I was going to have a bit more free time on Mondays, Wednesdays and Fridays and have already told myself I want to use this time to improve my photography, writing skills, website design and other projects I wanted to get done.

So I decided to audit the class. So basically I’m taking Linear Algebra without paying for the credits, doing any homework or taking any tests/quizzes. (Although I do foresee myself participating in this class since it’s a small class of eight people and the information is interesting.)

The big thing that struck me though, is my motivation for taking this class is almost purely curiosity. I’m not getting any credits for it and I can’t get credits for it if I would change my mind. I’m not entirely sure if I know what this means, if it means anything at all, or if this is worth thinking over in more depth.

I’m thinking that it comes down to a love of learning. I love to learn new things, I like hearing about new technologies, I find it interesting to look into things I know nothing about. The downfall to this is that I find myself knowing a very little about a very lot of stuff, which then becomes muddled in my mind and I end up knowing nothing about a lot, but I do remember that I knew something at one time.

This may require some rethinking.

I recently posted my equation for figuring out your current level of sanity. (See here.) As I have been thinking about it, however, I have thought that it would be best to generalize it so that it’s usable for people who are not in school. (The whole “desired grade minus current grade” thing didn’t sit right for me.)When trying to generalize this equation, however, I have discovered that this equation doesn’t seem to work as well as I first thought. I’m not saying that it is completely void, but I think it is good to note any inconsistencies or criticisms of my work. My original equation looked like this:

 Which I rationalized by saying that as the days of the semester came to a close, the students go insane because of all the homework and projects and tests that they have to deal with. (Stress from grades is accounted for as well.) This seems to work pretty well, I had several students tell me that they like the formula.

When you break it down to the most generic form, you find that it is simply:

 This also made some sort of sense. The more work that needs to be done, and the less time that is left to do the work produces the lowest feeling of sanity. (That is, the largest feeling of insanity.) On a side note, people are not always honest or accurate with predictions of work and/or time. So perhaps the equation should read more like:

But back to the generic equation, anyone with an understanding of physics should quickly recognize that:

 Which means that power and sanity are inverse each other.

 But this doesn’t make any sense at all. The more power you have, the more work you can get done per time period, the less sane you will be (or feel)?

My current conclusion is that the equation should not deal with the amount of work that a person needs to do in a certain time, but maybe something along the line of the number of events happening within a given time period. Each test, project and paper are then classified as events, but the equation is still generic enough to be applied to non-school-going people as well as holidays and vacations.

When I get my equation tweaked I’ll post it here. Until then, let me know what you think. 

UPDATE: I have discovered some issues with this equation, see my new posting here. I was thinking the other week, and developed the following formula for your current level of sanity. The main goal was to model sanity from a student’s perspective, but the formula may be tweaked for other occupations of lifestyles. Enjoy!

Math is like a roller coaster. It has high points and it has low points. Somedays everything works out tremendously nice and it’s the best thrill ever. Other days it’s a terrifying plunge in the dark that makes the stomach churn and the mind think, “Why on earth am I doing this? I’ll never do this again.”

I’ve had a bit of both today. It’s been up and down. It took me forever to get started, but when I did get going I got a few problems done, which I think is pretty good. Then I finished an assignment, and the downtime between assignments the feeling of finishing the work, and then trying to get started on the next assignment is the killer. It feels like I’m not getting anywhere. And it was during that break that I checked my email and found my math take home test sitting in my inbox, gleefully announcing that I had 7 days to finish it.

Unfortunately, the test is highly based on the 3 math assignments I have not yet completed, so the question is, which comes first the chicken or the egg? Do I do the assignments or the test?

I did, however, get an amazing kick out of a short little conversation I had today, it went something like this:

Guy: “Hey! What are you working on?”

Me: “Math.”

Guy: “Oh, what math?”

Me: “Real Analysis.”

Guy: “…oh… …what major are you?”

Me: “Communications.”

Guy: “… oh… … …”

Man, I just love that response from people. The class is almost worth it just for that.

Anyway, back to math…

FYI, the current year, that is to say 2007, is divisible (evenly) by 9. Trust me. And no, you can’t use a calculator to find out. I forbid it.

It’s not that hard folks! It’s simple division! Here, I’ll give you a hint, the number your currently looking for is between 222 and 224.

The geek in me comes out yet again, while doing my math homework.
For those who are not as math inclined as myself… which sums up to basically everyone else, barring the 4 people who are planning to major in math and the 7 others who teach it…

Anyway, when using a subscript of zero, the subscript is often referred to as “not”. (Or I suppose it could be “knot” for my purposes, I am saying it is “not”)

If this glowing description doesn’t make you want to run off and buy one, well… sorry, I’ll try to do better nextime.

Speaking of next time, there are more shirts on the way, we’ve got some great ideas coming in, so stay tuned for more news on the t-shirt front.

UPDATE: The image now links to the picture. My apologies to anyone who tried to access the shirt but couldn’t find it. Apparently I made an error when I input the image, and although I kept changing the link for the image, it kept changing it back.

It has come to my attention that Pi day is coming up! That’s right, 3-14 will be this upcoming Wednesday! But what good is Pi day, if you don’t have an “i 8 Sum Pi” Shirt?

Everybody who is anybody has an “i 8 Sum Pi” Shirt, and you need one, and soon.

For all of those people who have an “i 8 Sum Pi” Shirt, be sure to wear it this coming Wednesday!

Spread the word, Pi out!