Sylvester and Rachel live together on an island with two goods, food and shelter. Food is a private good and shelter is a public good. The utility function of Sylvester is U= Fs + 2(Zs+ Zr) where Fs is the amount of food he buys, Zs is the amount of shelter he buys and Zr is the amount of shelter Rachel buys. Similarly, the utility function of Rachel is U= Fr+ Zs+ Zr where Fris the amount of food she buys. Suppose the price of food is 10 and both Sylvester and Rachel have 100 to spend. Suppose also that it is not possible for Sylvester and Rachel to reach any kind of agreement. a. Determine the quantity of shelter they will buy and the efficient quantity of shelter if the price of shelter is 5? (Enter your answer in whole number.) Quantity of Shelter: Efficient 120 units b. What is the quantity of shelter they will buy if the price of the shelter is 15? (Round your answer to 2 decimal places (e.g., 32.16).) Quantity of Shelter: Not Efficient 30 units c. What is the quantity of shelter they will buy if the price of the shelter is 25? (Enter your answer as a whole number.) Quantity of Shelter: (Click to select) units d. What is the quantity of shelter they will buy if the price of the shelter is 35? (Enter your answer as a whole number.) Quantity of Shelter: (Click to select) units