1. Let there be two goods, x and y. The price of good x is $2, and the price of good y is $1. The consumer has income of $120. Good x has 50 calories per unit, and good y has 150 calories per unit. Besides the usual budget constraint, the consumer also has a calorie constraint: he is not allowed to consume more than 6,000 calories.

a. On a diagram with good x on the horizontal axis and good y on the vertical axis, show the set of bundles that satisfy the constraints that expenditure on the goods must not exceed income M = 120 and calories cannot exceed 6,000. Be sure to specify the bundles (x, y) at any intercepts or kinks.

b. Suppose the consumer's preferences can be represented by the utility function = + 3. What is the consumer's demand for x?