Lucie likes consuming candy (c) and fruit (f), and dislikes consuming plastic packaging (p), and has rational preferences over bundles (c, f, p). No matter how many units of each good she has, Lucie is always willing to exchange one piece of fruit for one piece of candy, and always has to be compensated by an extra piece of fruit for every piece of plastic packaging she has to consume. (a) Are her preferences monotone? Are they strictly monotone? If you answer yes, explain briefly (no need for a formal proof). If you answer no, provide a coun- terexample. (b) Are her preferences strictly convex? If you answer yes, explain briefly (no need for a formal proof). If you answer no, provide a counterexample. (c) At Lucie's local supermarket, each candy is wrapped in 2 pieces of plastic pack- aging, and so is each piece of fruit. Her income is $60 and each (wrapped) piece of fruit and (wrapped) candy costs $4. When she chooses optimally, Lucie con- pieces of fruit, and pieces of plastic packaging. Show working/explanation for your answer. sumes pieces of candy, (d) Lucie finds a small organic market that sells 4 candies in 1 piece of plastic packag- ing, and sells fruit with no plastic packaging. Each wrapped container of 4 candies costs $20 at this market, and each unwrapped piece of fruit costs $6. When she chooses optimally, Lucie consumes pieces of fruit, and pieces of plastic packaging. Show working/explanation for your answer. pieces of candy,