On january 1, professor smith made a resolution to lose some weight and save some money. he decided that he would dedicate a $100 budget for lunches each month. for lunch, he has only two choices, the faculty club, where the price of a lunch is $5 and alices restaurant, where the price of lunch is $10. every day that he does not eat lunch he runs 5 miles. a) assuming that professor smith spends the $100 each month at either alice's restaurant or the club, sketch his budget constraints. show actual numbers on the axes. b) last month professor smith chose to eat at the club 10 times and at alice's 5 times. does this chose fit within his budget constraints?