Anthony spends his income on fishing lures (L) and guitar picks (G). Lures are priced at $2, while a package of guitar picks cost $1. Assume that Anthony has $30 to spend and his utility function can be represented as (, ) = ^0.5^0.5 . Anthony's goal is to maximize his utility from the consumption of fishing lures (L) and guitar picks (G). [1] a. What is Anthony's budget constraint? [2] b. What is the Lagrange function to solve for Anthony's optimal number of lures and guitar picks? [3] c. Find the partial derivative with respect to the L, G and from the Lagrange function. [4] d. What is the optimal number of lures and guitar picks for Anthony to purchase?