In the city of Producton, there are two uses for land: Factories and Houses. There is a train station at the city center (3: = 0). We will study land use from 3: = 0 to 3: = 50. Factories ship outputs to the train station, and this is more expensive the farther the factory is from the station. Factory prots are given by 7T 2 100 4d, R, where (it is distance to the station, and R is rent paid by the factory. Households like living near the city center: household utility for living at location x is given by U = 6001} R. In this equation, R represents the rent paid by the household. If households moved out of the city, living in the countryside would give the household U0 2 0. a raw a 1 -rent lagram Wit an 15, t e 1 rent curves or actories an ouse o s, respective y. D b'd d' 'hbf db h b'd f f ' dh hld ' 1 Label the bidrents at a? = 0. (b) Describe precisely the land use in Producton. You should provide numerical answers and say which land is used for what purpose. The train station stops shipping cargo for the factories. In its place, factories now have to ship output to the highway. Their prot function now becomes 7T' 2 100 2th, R, where (1;, is distance to the highway, located at m = 50. (c) Describe the new land use in the city. You should provide numerical answers and say which land is used for what purpose. (d) Draw a different diagram with the equilibrium rent patterns in Producton, after factories start shipping output to the highway