Charlie's utility function for his consumption of apples xA and bananas xB is u(xA, xB) = xAxB.
If the price of apples is pA = 3 and the price of bananas is pB = 1, and Charlie has $12 to spend on apples and/or bananas, then:
The budget equation is
3xA+xB=12
And the optimization condition (to maximize Charlie's utility) is
-xBxA=-3
Given these two conditions, find Charlie's optimal bundle: (xA*, xB*) =