My study methods: Effective?

At SOM, our professors are kind enough to supply us with previous years' exams, which is also terribly unkind, as the extra study materials ruin the weekend by (a) taking away excuses to not work, and (b) making John feel stooooopid.

Take Microeconomics. Please! How I cry when I simply cannot proceed with a problem. But practice makes perfect, and now I can invent problems and then solve them! Let's do just that.

Suppose I want to start a business selling chocolate milk. I can produce the milk using a machine that has two speeds, low and high. For whatever reason, it has to run at that speed all day, it can't switch midday. The slow machine makes 100 gallons/hour, costs $90/hour in labor and uses 2 oz. of the magic chocolate ingredient per gallon. The fast machine makes 120 gallons/hour, costs $120/hour in labor and uses 3 oz. of the magic chocolate ingredient per gallon. The ingredient costs $0.16 an ounce.  The machine is being lent to me for free for 12 hours/day. How does the market price of chocolate milk determine the speed at which I run my machine?

Funny you should ask:

LOW SPEED (100 gallons/hour)
Makes 1200 gallons/day
Therefore costs $1080 in labor/day
And costs $384 in secret ingredient/day
Average Variable Cost (AVC) = Total Variable Cost (TVC) / Quantity (Q) =  ($1080 + $384) / 1200 = $1.22

HIGH SPEED (120 gallons/hour)
Makes 1440 gallons/day
Therefore costs $1440 in labor/day
And costs $691.20 in secret ingredient/day
Average Variable Cost (AVC) = Total Variable Cost (TVC) / Quantity (Q) =  ($1440 + $691.20) / 1440 = $1.48

The answer is that you would not start manufacturing this chocolate milk until the market price is $1.22. Then you should run it at low speed and make up to 1,200 gallons/day. Keep doing that until the market price rises to ($1.48 x 1440 - $1.22 x 1200) / (1440 - 1200) = $2.78. At that point, switch to the high technology and run it at full capacity. The reason you should wait until the market price gets that high is because there's an opportunity cost to running at high-speed. That's the part that's a little counter-intuitive. For example, if the market price were $2, you might think you should run at high speed. But if you run at low speed you sell 1200/day for $2 each, making $2400 at a cost of $1464 for a profit of  $936. But if you run the high machine you'll sell 1440/day for $2 each, making $2880/day at a cost of $2131.20. Still profitable, but the profit is only $748.80. So it only becomes worthwhile to run at high and incur those costs when the profits offset them enough to make it a better alternative than running slow. If the market price is $3 for example, running on high you'll earn a daily profit of $2188.80, vs. $2136 at the low speed.

Ain't that something?