Jump back to one of the following links:    Home     Courses   Tutorials      Misc

Jump to one of the following dimensional analysis parts:   Choose One Introduction to Dimensional Analysis Part 1- The Need for Units Part 2- Setting up Conversions Part 3- Basic Conversion Problems Part 4- Complex Conversion Problems Part 5- Problem Dissection I Part 6- Problem Dissection II Part 7- Density Problems Part 8- Quizzes

To contrast the previous problem, how about a more practical one? Let's say that your goal is to purchase the most economical laundry detergent you can find at the local X-Mart (hey, I don't want to be seen promoting any of the whatever-marts). No other guidelines but the cheapest you can find. Let's analyze the problem as we go.

Here's what you initially see-

If all you were asked to do was to spend the least amount of money, then you'd choose between Brand C and Brand D for $3.23. If the different brands are packaged in the same quantity, then it's a fairly easy decision to pick the least expensive product. Ah, but that would be way too easy! Many times the product comes in different quantities not only across different labels but within the same label. Hopefully, you've learned by now the commonly believed idea that buying in bulk is cheaper really isn't always true. For instance, my wife and I were grocery shopping many years ago and we needed to get some powdered formula for our daughter. The choices we had were $5.50 for 12 ounces and $14.97 for 32 ounces. Let's see how they work out-

12 oz Container:
32 oz Container:

Granted, it's not much of a difference; but, it adds up. Just for grins, let's figure out the price difference per year if we assume someone with twins and an average of five 12 oz containers of powdered formula a week for one year-

OK, it ain't the national debt, but if you add up savings like that over numerous products over the span of a year, paying attention to savings like these will amount to a significant dollar amount. Unlike what a certain popular commercial states, everybody knows that it doesn't always pay to shop in bulk.

Maybe that's how we should look at the laundry detergent. Let's take it on a price per ounce viewpoint and see what shakes loose-

1.	Brand A	$3.98/100 oz
2.	Brand B	$4.98/100 oz
3.	Brand C	$3.23/125 oz
4.	Brand D	$3.23/125 oz
5.	Brand E	$4.47/69 oz
6.	Brand F	$10.97/200 oz
7.	Brand F	$6.64/100 oz
8.	Brand G	$5.97/100 oz

Once again it seems to be a toss-up between Brand C and Brand D as displayed. If you have purchased laundry detergent, however, you know that it's not the quantity of detergent you have but how many uses are in the container. Let's redisplay the information in price per use instead of price per ounce-

1.	Brand A	$3.98/32 uses
2.	Brand B	$4.98/32 uses
3.	Brand C	$3.23/24 uses
4.	Brand D	$3.23/28 uses
5.	Brand E	$4.47/42 uses
6.	Brand F	$10.97/52 uses
7.	Brand F	$6.64/32 uses
8.	Brand G	$5.97/54 uses

Ah, ha! And now we see that Brand E wins as the most economical choice of laundry detergent. Not that I'm suggesting you should buy this based solely on price. Quality of product plays an important part in shopping in addition to price. We'll leave that up to the economics classes to discuss ideas like utility...