Lionel likes to consume soccer shoes (S) and soccer balls (B), and he has the following utility: U (S, B) = S 1/2 B 1/2 Suppose Lionel wants to achieve a minimum utility of U, and he wants to choose consumption of S and B that minimize his consumption but achieves that level of utility. The prices of shoes is p S , and the price of balls is p B . a) Write down the lagrangian that solves Lionel's expenditure minimization problem. b) Solve for the optimal consumption (i.e. hicksian demand) for S and B for a given level of prices and utility