[40 points] In Retireland, no one commutes to work, and everyone consumes a single good (food), which is imported from another region and can be

[40 points] In Retireland, no one commutes to work, and everyone consumes a single good (food), which is imported from another region and can be purchased (one meal at a time) from the nearest vending machine. Alternatively, food can be delivered by a distant catapult, capable of flinging a meal through a food slot on the customer's roof. The price of a delivered catapult meal is $8 and the price of a vending-machine meal is $2. The travel cost for consumers is $1 per roundtrip mile ($0.5 per mile traveled). 

a. How many miles would the market area (i.e. maximum miles to be traveled for vending) for the vending machine be?

b. Show your answer in a martini shaped glass, indicating the slope of the glass' arms, price of food at vending machine, and the radius of the city. (Label your axes)

c. Now assume that everyone owns a bike, which reduces the travel cost to $0.2 per round-trip mile. What would the new market area be for the vending machine?

d. Continue from part c above (everyone owns a bike still). Assume that a new vending machine replaces the old one, now allowing customers to purchase 2 meals at a time (meals are storable at no cost). How would that affect (if any) the market area of the vending machine?

e. Continue from part d above, and assume that everyone eats 2 meals per day in this town, and a month is 30 days long. What would the monthly rent difference be for a residence located 5 miles v. 10 miles away from the vending machine? (Hint: a single daily trip to the vending machine is sufficient).