Please answer this question for me!

2. (10 points) Consider a two commodity world and a particular consumer in two different situations. In situation 1, he has income m = 12$, price of commodity 1, p1 = 1$, and price of commodity 2, p2 = 1$. This consumer then chooses the commodity bundle ($1, X2) = (8, 4), i.e., 8 units of commodity 1 and 4 units of commodity 2. Observe that in Situation 1, the bundle (21, 12 = (8, 4) exhausts his budget. Now we move to situation 2 where, the same consumer has income m' = 16, p1 = 1 and p2 = 2. In this situation the same consumer chooses the commodity bundle (21, 22) = (6,5), i.e., 6 units of commodity 1 and 5 units of commodity 2. Observe that in this situation, (i.e. Situation 2), the bundle (21, Z2) = (6, 5) too exhausts the budget. (a) Does the chosen bundle in Situation 1 , (1, 12) satisfy the budget constraint in Situation 2 ? (2 points) (b) Does the chosen bundle in Situation 2 , (21, 22) satisfy the budget constraint in Situation 1 ? (2 points) (c) Now, one of the fathers of consumer choice theory, Professor Samuel- son, suddenly arrives and claims that this consumer's choice is not consistent with Utility maximization. Is Professor Samuelson right? Or wrong ? Or is there insufficient data to make any con- clusion ? Prove or disprove with adequate reasoning. (6 points)