Hi! Please help. Computations needed

Ex 6.1: Optimization with Quasilinear Utility Suppose that Charlene can produce either fish (good 1) or coconuts (good 2) according to the production functions x1 = 421, X2 = L2 In other words, if she spends Li hours producing fish and L2 hours producing coconuts, she will produce (and consume) $1 = 4L1 fish and X2 = L2 coconuts. Charlene has decided to work 75 hours per week. (a) Draw Charlene's PPF with clearly labeled axes, and derive the expression for her MRT. (b) Suppose Charlene's preferences are given by the quasilinear utility function u(X1, 12) = 100 In 1 + 2 What is the MRS of this utility function? What is the MRS at the endpoints of her PPF? (c) Find Charlene's optimal bundle. Draw Charlene's PPF, her optimal bundle, and her indifference curve passing through that optimal bundle. Ex 6.2: Optimization with Perfect Complements Charlotte can produce tea (good 1) and biscuits (good 2) according to the production functions *1 = f1(LI) = VLI $2 = f2(L1) = 2VL2 She devotes 25 hours of labor to producing these two goods. (a) Derive the MRT and draw the PPF with clearly labeled axes. (b) Suppose Charlotte's preferences were given by the utility function u(x1, (2) = min {321, 2.2} What is the MRS of this utility function? What is the MRS at the endpoints of her PPF? (c) Find Charlotte's optimal bundle. Draw Charlotte's PPF, her optimal bundle, and her indifference curve passing through that optimal bundle