This year I will have 180 hours free in which I can watch TV or watch movies. Each movie lasts 2 hours, and I'll be able to watch each TV show for 20 hours. I have $600; each movie costs $10, and each game costs $40. (a) If I make 3 new friends every time I get a new video game, and 1 new friend every time I watch a movie, how many movies should I watch this year to maximize the number of new friends I make?
(b) If I instead make 5 new friends every time I get a new video game but I still make 1 friend per movie, then how many movies should I watch this year to maximize the number of new friends I make?
(c) Suppose I want to make as many new friends as possible. What is the smallest whole number of new friends each new video game must give me (assume I make the same number of new friends for each game I buy and that I make 1 friend per movie) in order for it to make sense for me to buy only video games this year?