Problem:
Luke likes to consumer CDs (good1) and pizzas (good 2). His preference over both goods is given by the utility function
U(x1; x2) = x12x24.
If Luke allocates $200 to spend on both goods and if a case of CDs costs $20 and a pizza costs $10, how many cases of CDs and pizzas would he consume in order to maximize his utility subject to his income? Show your work and illustrate your answer graphically.
Additional Information:
The problem belongs to economics in price theory deals with deriving maximum marginal utility and marginal rate of substitution.