Lulu has a utility function of U(X,Y) = (5X + 3Y) for goods X and Y. Assume that she is a utility maximising consumer who spends all of her weekly budget of $18 on goods X and/or Y. The price of good X is $1.50, while the price of good Y is $1.

(a)Calculate Lulu's best affordable bundle by using her MRS, relative prices and comparing these slopes.Explain your answer.(3 marks)

(b)Prove that the bundle you calculated in(a)above isLulu's best affordable bundle by calculating the utility per dollar spent on each good.(2 marks)

(c)Plot Lulu's budget constraint and indifference curve on a set of axis showing her best affordable bundle.(2 marks)

(d)Calculate Lulu's level of utility at her best affordable bundle.(1 mark)

(e)Explain what happens to Lulu's marginal rate of substitution as you move down her indifference curve? As part of your answer, explain what marginal rate of substitution means(2 marks)

(f)Give one assumption of well-behaved preferences that Lulu's utility function does not meet, and explain why it does not meet that assumption(1 mark)