Here's an update to my previous post, explaining some of the things I left out.

I assume that Hockett used the formula for the Average Total Cost to create the graphs in the original graph. I used the formula found at about.com:

Average Total Cost = Fixed Costs/Quantity + Variable Costs

In the case of the ceramic mug, that would be AC = 14/Quantity + 0.18 since each mug costs 14 mj to make and 0.18 mj to clean after each use. Here are the other formulas I used to recreate the graph:

Foam: AC = .2 (There are no variable costs, and a new foam cup is used every time)

Paper: AC = .55 (See foam.)

Glass: AC = 5.5/Quantity + 0.18

Plastic: AC = 6.3/Quantity + 0.18

To find the area under the curve for, I used an Excel plug in from Boomer.org--scroll down to "PK Functions for Microsoft Excel".~~You can use the area under the curve numbers to calculate just how many mjs you would save by using ceramic, glass, or plastic instead of foam or paper.~~

Using a ceramic mug twice a day for about 2 years will save 1,639 MJ over using foam cups. That's a savings of 8,195 foam cups (1639/.2)! Still, your better bet is the plastic coffee mug which saves you 13,112 MJ over those 2 years--65,560 foam cups!

See Peter's correction in the comments!

## Wednesday, April 18, 2007

### Eco-update

Labels:
applied math,
energy,
Green choices

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## 3 comments:

I don't understand how you're getting to your conclusions.

Using a ceramic cup twice a day for two years uses this energy:

14 MJ + (0.18 MJ * 2 * 2 * 365) = 276.8 MJ

Using foam cups consumes:

0.2 MJ * 2 * 2 * 365 = 292 MJ.

The difference is equivalent to 76 foam cups.

Doh! You're right. I was calculating the area under the curve. That's a running total of all the average costs. But I should have just been looking at the final points for both curves.

I knew I was going to make a mistake. Thanks!

I realize now what confused me. The area under the curve is the total energy cost for the foam cup because it's a flat line. The final point is the upper right-hand corner of a rectangle, whose area gives you the total energy used:

Total Cost = .2 * Quantity.

However, the area under the Ceramic curve is not the same as the total energy cost since the Average Total Cost changes with the number of uses.

Total Cost = 14 + .18 * Quantity.

Again the final point on the Total Average Cost curve is the upper right-hand corner of a rectangle whose area is the total energy cost.

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