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Assume that a consumer’s satisfaction depends upon leisure (L) and income (Y), so that the utility...

Assume that a consumer’s satisfaction depends upon leisure (L) and income (Y), so that the utility function is:
U = 48L + LY – L2
Let N denote the hours of work by the consumer and W the hourly wage rate. Consequently, Y = WN and L + N = 24.
If the hourly wage rate is $15 per hour:
a) What are the utility maximizing hours of leisure, L*?
b) What are the utility maximizing hours of work, N*?

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