$2\mathrm{.}5$ Ms$.$ Caffeine enjoys coffee $(C)$ and tea $(T)$ according to the function $U(C,T)=3C+4T.$

a$.$ What does her utility function say about her MRS of coffee for tea? What do her indifference curves look like?

b$.$ If coffee and tea cost $$3$ each and Ms$.$ Caffeine has $$12$ to spend on these products, how much coffee and tea should she buy to maximize her utility?

c$.$ Draw the graph of her indifference curve map and her budget constraint, and show that the utility$-$maximizing point occurs only on the $T-$axis where no coffee is bought.

d$.$ Would this person buy any coffee if she had more money to spend?

e$.$ How would her consumption change if the price of coffee fell to $$2?$

CAN YOU SHOW THE WORK AND GRAPH PLEASE THANK YOU SO MUCH!