Question 4 Mary consumes only scoops of ice-cream {I} and cones {3:}. She insists on s particular combination of ice-cream and cones. Mary must have 2 scoops of ice cream with every cone. Assume that both quantities of icecream scoops and cones are continuous variables. Her preference is completeI transitive, and monotone. {a} {5 mental Prapose 2 diiferent utility functions that represents Mary"'s preference. {b} Pick one of the utility functions you proposed in part {a}. {i} (5 marks) Draw a couple of indiiference curves, indicate two bundles in each of them and the corresponding utility level. Make sure to label the axm appropri ately. {ii} ['5 marks} What is the Marglnal Rate of Substitution for these preferences? Explain. {c} Suppose each scoop of icecream costs $2, and each cone costs $1. Mary has an icecream budget of $111]. {i} (5 marks) Draw her budget line in the diagram you have drawn in part [b]. Show your work. {ii} ['5 marks} Find Mary's utility maximising consumption bundle. Show your work. {d} Suppose that now there is a promotion that each scoop of icecream is only $1. Everything else remains the same. {i} (5 marks} Redraw the diagram from part {c} AND draw the new budget line as a result of this promotion. Label all the intercepts appropriately. {ii} ['5 marks) Compare Mary's new budget set to her old budget set. 'Which one is larger? lustrate your answer. {iii} (5 manta) Assume now that she can only consume integer quantities of :r and 3:. Find Maryis new utility maximising consumption bundle. Show your work