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Sheila's income and leisure preferences can be expressed by U( C, L ) = 2 x ( YL - 40C - 100L ) This utility function implies that Sheila's marginal utility of leisure is 2Y - 200 and her marginal utility of income 2L - 80. In a week, there are 168 hours available for her to allocate between work and leisure. Sheila earns $10 per hour after taxes and receives $120 worth of welfare benefits each week during the pandemic regardless of how many hours she decides to work. Assume that the price index is 1. a) What is Sheila's budget line? b) What is Sheila's marginal rate of substitution when L = 100 and she is on her budget line? c) What is Sheila's optimal relationship between income and labour hours? d) What is Sheila's optimal amount of labour hours, leisure hours, and income? e) At the optimal allocation, what is Sheila's utility level? Show your work