If your income is $18.00 and the prices of x and y are $4.00 and $2.00, respectively, what quantities of each will you purchase to maximize utility?

2 units of X and 5 units of Y

Step-by-step explanation:

(a) Utility is maximized when (MUx / Price of X) = (MUy / Price of Y)  

This condition holds for the following cases

1.  X = 4 (MUx / Px = 8 / 4 = 2) and Y = 6 (MUy / Px = 4 / 2 = 2)

2.  X = 2 (MUx / Px = 16 / 4 = 4) and Y = 5 (MUy / Px = 8 / 2 = 4)

For the first case Total cost = 4 x $4 + 6 x $2 = $(16 + 12) = $28 (Budget is exceeded).

In the second scenario, Total cost = 2 x $4 + 5 x $2 = $(8 + 10) = $18 (budget is exhausted).

Optimal case contains  X = 2 units, Y = 5 units.