Suppose Bilbo Baggins spends all of his income on food F, and pip… Show more (U(F,W)=(2F^{1/2}+2W^{1/2})^{2}) Suppose Bilbo Baggins spends all of his income on food F, and pipe weed W, and his utility function is given above. If Bilbo%u2019s income is Y=144, the price of food is (p_{F}=$4) and the price of pipe weed is (p_{W}=$2) : a) Assuming pipe weed is plotted on the %uD835%uDC66-axis, find Bilbo%u2019s marginal rate of substitution and the marginal rate of transformation he faces. b) Assuming an interior solution exists, solve for the Bilbo%u2019s optimal bundle of food and pipe weed using just the marginal rates of substitution and transformation and Bilbo%u2019s budget constraint. • Show less