(1) Pass me the water! An African family that consumes W gallons of water every year, more or less the same amount every day. The price of water is P_W dollars per gallon. The water is in a store located far away, so they go to the store and purchase large amounts of gallons which they store in their house. Every time they drive their truck to the store to purchase water they use up l|.l gallons of gas. The price of gas is P5. Let rn be the average amount of gallons they have In the house (m stands for mean) and M be the VALUE in dollars of those gallons. o (1) Imagine that the family decides to go to the store to buy water once a year. How many gallons will they purchase? What is the average amount of gallons they will have stored in the house? How many dollars will those gallons be worth? 0 (2) What if it decides to go four times a year? What is m in this case? What is M if the family decides to go to the store N times? The family has access to a bond market. All the dollars that it has invested in stored water could be earning the interest rate R. o (3) Is R nominal or real? 0 (4) The total cost of purchasing water is the price times the quantity, plus the cost of going to the store N times, plus the interest lost. Write down the total cost as a function of M. (5) Find the M that minimizes the total cost of purchasing and storing water. 0 (6) How does the average amount of money invested in water, M, depend on the total amount of gallons consumed at the end of the year, W? How does it depend on the price of gas, PG? How does it depend on the cost of each trip to the store, In? Explain intuitively? o (7) Does the amount of 1iiilrater stored depend on the interest rate? (8) How does the average amount of money invested in water, M, depend on the price of water, PW '? e (9) How does the REAL amount of water (that is, the amount of gallons, m) depend on PW ? Is your answer different from (8)? If so, explain why intuitively