Mgccl's Ivory Towerso tired

Since I have my own credit card, it's my nature to shop for food and act Chinese by being cheap.
Eggs is a must for my diet, so I found 2 packages, one is for 12 extra large eggs, 27 ounces, $1.79. The other is 12 jumbo eggs, 30 ounces, $1.99.
I did some division
27 ounce/$1.79 = 15.0837989 ounce per dollar
30 ounce/$1.99 = 15.0753769 ounce per dollar

Clearly, buy extra large eggs is better, I get 0.008422 once more every dollar I spend!
Or is it?

I forgot one thing that could entirely change this simple easy math problem into sophisticated money saving skill.
I don't eat egg shell.
suppose, egg shell have a constant density, which is really possible because it's 95% CaCO₃, d_s(shell and d_e for the entire egg) with 2 shell volumes, V_sl(extra large shell) and V_sj(jumbo shell)would large eggs still be the better choice?

27 ounce - d_s*V_sl/$1.79 ???? 30 ounce - d_s*V_sj/$1.99

so, you can see, what determines everything is the growth of the egg shell's mass VS the growth of the entire eggs mass. The egg's shape is different, but it's possible to see that it can be cut into infinite many infinite small height cylinders, or just consider it as a circle. All I need to do is to prove that for every circle, the increase of the area(the mass = volume * density, and we made volume into area and the ignore the density because the same for all shell) of the entire circle is far greater than the increase of the area of the ring (the shell). This idea always works if the volume of the egg approaches infinity, even though it's not proven to work in this situation, but it's nice to analyze and can come out with some formula that might help with us afterward.

the circle's radius is r, ring's width is w, the equation for the circle's area is:
πr²
for the ring's area is
πr² - π(r-w)²
suppose egg shell's size don't increase (likely, at most, it won't increase more than 1.2 times of it's original width), then the only variable is r. and then you could see, the circle's area grows quadratically, while the ring's area grow linearly.
πr² - π(r-w)² = πr² - πr²+π2rw-πw² = π2rw-πw²
As the egg's volume grow larger, shell's volume proportion to egg's volume gets smaller.

Without knowing each variable's value, the only thing we can use is common sense.
set up this equation
27 - d_s*V_sl/1.79 < 30 - d_s*V_sj/1.99
now solve it
1.99*(27 - d_s*V_sl) < 1.79(30 - d_s*V_sj)
53.73 - 1.99d_s*V_sl < 53.7 - 1.79d_s*V_sj
0.003 - 1.99d_s*V_sl < -1.79d_s*V_sj
1.11173184d_s*V_sl - 0.00167597765 > d_s*V_sj

If this holds, then it's better to buy jumbo eggs. is this likely? I don't know, but I believe it's yes. When the volume of the shell increase less than 11% and the egg's volume increase from extra large to jumbo (11%), it is most likely to be true because the constant number is extremely small.

I bought the jumbo eggs. What will you do? btw, price in your area will differ, maybe it's better to buy extra large eggs after all.

Tsung recently creates a new service, SiteTag. The service require a bit of Javascript embedded in the website, It finds out the most popular keyword for your site from referrals, and calls them tags. My profile page shows 2 days of data collected. It doesn't look really impressive, since the common English prepositions are counted as tags...

Because this is a new service made in a hurry, I can see the future improvements, small bugs will be fixed really soon. My talk with Tsung clearly states that any suggestion will be taken seriously. Wish the future of SiteTag be bright.