Slash spends his income on strings (S) and guitar picks (G). Strings are priced at $2, while a package of guitar picks cost $1. Assume that Slash has $30 to spend and his utility function can be represented as U(S,G) = S0.5G0.5 For this utility function, MUS = 0.5S0.5G0.5 and MUG = 0.5S0.5G0.5.

1. (a)What is the optimal number of strings and guitar picks for Slash to purchase? How much utility does this combination give him?
2. (b)If the price of guitar picks doubles to $2, how much income must Slash make to maintain the same level of utility?