Beer and beach visit Peter only enjoys beer and visiting the local beach. His utility function is described by

u(x1; %2)= 0.2lnx1 + 0.8lnx2

where x1 is the amount of beer and X2 is the number of trips to the beach. A bottle of beer costs $2; a trip to the local beach costs $1. Peter has a budget of $20. Answer the following questions both numerically and graphically.

(a)Please derive Peter's marginal utility for beer and beach visits respectively. What is the marginal rate of substitution?

(b)Please derive the budget line.

(c)What is the optimal choice for Peter?