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Consider a simple economy with only Robinson Crusoe, coconuts and leisure. He has utility U (c,l) = c^(1/2)*l and a production function C=L^(1/2), where c is the amount of coconuts he consumes, l is the amount of leisure he consumes, and L is the amount of labor he puts in collecting coconuts. He only has 24 hours a day such that l = 24 - L.
In this exercise you will first find the optimal choice of (c,l,L) for the lonely Robinson.
Use the production function and time restriction to express U(c,l) only as a function of L. Once you have done that, find Robinson's optimal amount of labor, L*. Use L* to find c* and l*, doing this you will have a full characterization of Robinson's behavior.
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