Calculating Optimal Work Hours
An individual's satisfaction is described by the utility function U(t, y) = 4√t + y, where 't' is hours of free time and 'y' is units of a consumption good. The individual is self-sufficient, and their production of the good is determined by the function y = 8√h, where 'h' is hours of work. The total time available per day is 24 hours, so t + h = 24. Using calculus, determine the optimal number of hours this individual should work to maximize their utility.
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