1. A consumer, Sam, finds only three products, X, Y, and Z, are for sale. The amount of utility which his consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend.

	Product X			Product Y			Product Z
Quantity	Total Utility	Marginal Utility	Marginal Utility per $		Quantity	Total Utility	Marginal Utility	Marginal Utility per $		Quantity	Total Utility	Marginal Utility	Marginal Utility per $
1	42				1	14				1	32
2	82				2	26				2	60
3	118				3	36				3	84
4	148				4	44				4	100
5	170				5	50				5	110
6	182				6	54				6	116
7	182				7	56.4				7	120

1. Complete the table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places.
2. How many units of X, Y, and Z will Sam buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (Hint: Remember to use MU from the last unit sold.)
3. X = Y = Z =
   

MUZ MUY Pz MU PY Px