2) Shelly's preferences for consumption and leisure can be expressed as U(C, L) = C * (L -20).~ There are 120 hours in the week available to split between work and leisure. Shelly earns $10 per hour after taxes. She also receives $500 worth of welfare benefits each week regardless of how much she works. ~ a) Graph Shelly's budget line. ~ b) What is Shelly's marginal rate of substitution(MRS) when L = 100 and she is on her budget line? Hint: MRS = abs(dC/dL) = U/(L-20)^2- c) What is Shelly's reservation wage?~ d) Find Shelly's optimal amount of consumption and leisure.~