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Luke only consumes strawberries (S) and turnips (T) each week with his $36 income. The price of strawberries is PS = $3/basket, while the price of turnips is PT = $1.50/turnip. Luke's preferences are given by the following utility function

U(S,T) = sqrt(ST)

(a) Set up the Lagrangian equation for this constrained maximization problem.

(b) What are the 3 first order conditions (FOC) of optimization from the Lagrangian?

(c) Find Luke's optimal consumption bundle of strawberries and turnips.

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