On January 1, Professor Smith made a resolution to lose some weight and save some money. He decided that he would strictly budget $100 for lunches each month. For lunch, he has only two choices: the faculty club, where the price of a lunch is $5, and Alice's Restaurant, where the price of a lunch is $10. Every day that he does not eat lunch, he runs five miles.

1. Assuming that Professor Smith spends the $100 each month at either Alice's or the club, sketch his budget constraint. Show actual numbers on the axes.
2. Last month Professor Smith chose to eat at the club ten times and at Alice's five times. Does this choice fit within his budget constraint? Explain your answer.
3. Last month Alice ran a half-price lunch special all month. All lunches were reduced to $5. Show the effect on Professor Smith's budget constraint.