Suppose Joe's utility for lobster (L) and soda (S) can be represented as U = L ⁶ S ^0.4. Joe walks into a restaurant with $400. Lobsters cost $40 each and sodas cost $1 each. Calculate the number of lobster and soda will Joe consume if he intends to maximize his utility. (There are no tax and no tips.) Make sure you show your work starting with the utility maximization condition. No shortcuts.

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