5. A peasant has utility U(B,C) = 4B+C over bread B and flourless cake C, with marginal utilities MUB = 2/B and MUC= 1. Prices are p = 2 and pc = 3, and his income is I = 33. First, double-check that he initially consumes (B,C) = (9,5), with utility U = 17, and illustrate on a budget/indifference curve diagram. Next, benevolent monarch Marie Antoinette learns that carbs are evil. She wants to discourage bread consumption without making the peasant worse-off. To this end, she taxes bread, tripling its total price to p = 6, while also scattering a lump sum of gold coins in the dirt, thereby raising his income to I' = 33 + L. Determine how many gold coins L she must give him if she wishes to leave him just as happy (U= 17) as he was before. Show this whole situation on a diagram. (A good diagram will help you figure out how to find L.) Is the lump sum L. big enough for him to afford his old consumption bundle (9,5)? Explain.