$2.$ Elmo finds himself at a Coke machine on a hot and dusty Sunday. The Coke machine requires exact change two quarters and a dime. No othercombination of coins will make anything come out of the machine. No stores are open; no one is in sight. Elmo is so thirsty that the only thing he cares about is how many soft drinks he will be able to buy with the change in his pocket; the more he can buy, the better. While Elmo searches his pockets, your task is to draw some indifference curves that describe Elmo's preferences about what he finds.$($a$)$ If Elmo has $2$ quarters and a dime in his pockets, he can buy $1$ soft drink. How many soft drinks can he buy if he has $4$ quarters and $2$ dimes? $[($b$)$ Does Elmo have convex preferences between dimes and quarters? $($c$)$ Does Elmo always prefer more of both kinds of money to less? $($d$)$ Does Elmo have a bliss point? $($e$)$ If Elmo had arrived at the Coke machine on a Saturday, the drugstore across the street would have been open. This drugstore has a soda fountain that will sell you as much Coke as you want at a price of $4$ cents an ounce. The salesperson will take any combination of dimes and quarters in payment. Suppose that Elmo plans to spend all of the money in his pocket on Coke at the drugstore on Saturday.Draw one or two of Elmo's indifference curves between quarters and dimes in his pocket. Describe these new indifference curves in words.