The utility-maximizing bundle of goods is found at the point of tangency between the budget constraint and an indifference curve.
In the following diagram, the utility-maximizing bundle is the one labeled point K. There are two different, but equally important, ways to interpret this point.
a. Of the three points on the consumer's budget constraint (J, K, and L), what makes K special?
b. Of the three points on the consumer's indifference curve (M, K, and N), what makes K special?