How much will the landlord charge to rent 1 acre at the city?

1.     Consider the simple von-Thunen model of agricultural land use developed in class. This question asks you to analyze the land use of carrot farmers who use a fixed proportion production technology. Assume the following:
— carrot yield (E) is 20 tons per acre
— carrots sell at $15 per ton (P) at the market
— non-land input costs (I) are $60 per acre
— transport cost (t) is $4 per ton per mile
— farmers pay the transport cost of moving carrots d miles to the market

a.   (6 points) Derive the bid-rent curve per acre of land for carrot farmers by imposing the appropriate long-run equilibrium condition. Explain the condition. Show all steps.
b.  (6 points) Plot the bid-rent curve for carrot farmers. Then calculate the land area where carrots are grown.
c.      (4 points) How much will the landlord charge to rent 1 acre at the city? at d=1 mile? at d = 5 miles? Show computations.
d.     (4 points) Where does Farmer Jones prefer to locate? Why