a) In Figure S.1.4, the area under the budget line corresponds to all baskets a consumer can choose, given her income and the prices.
b) The curves I1, I2, and I3 in Figure S.1.4 are three of the consumer's indifference curves for the two goods.
c) The consumer wants to end up on an indifference curve as far to the northeast as possible.
She also has to afford it. The only indifference curve she can both afford and that is as far as possible to the northeast is I2. The only point on I2 she can afford is point A. The basked corresponding to point A is therefore the only utility maximizing choice she can make in this case.
d) It is possible to construct situations in which a consumer can find several points that all maximize her utility. Take the case of perfect substitutes. In Figure S.1.5, we have four indifference curves for perfect substitutes. Suppose that the prices of the goods are the same (which is reasonable, since they are perfect substitutes). That means that the budget line, the broken line, will be a straight line with the same slope as the indifference curves. The consumer can then choose any point on the budget line. They all maximize her utility.
Note that, if one of the goods is more expensive than the other one is, the budget line will no longer have the same slope as the indifference curves. Say that good 2 is cheaper than good 1. Then the budget line will be steeper, for instance as the dotted line in the figure. The consumer would then choose to consume only the cheaper good, i.e. good 2. A solution such as this, when one ends up at one of the axes, is called a corner solution. In such a case, the criterion that MRS = MRT is no longer valid.