EC330 P501 Due Thursday October 14th - Page 6 of 11 Su2021 8. (6 points) The city of Springfield lies at the east end of a railroad. To the west, there are one hundred miles of plains along which there are several towns-all connected to by rail. To the east of Springfield are fifty miles of mountains, whose small villages are connected by a few winding dirt roads. The only factory in the region is in Springfield. It produces widgets at a cost of $20 per unit at the factory door. Thanks to the rail line, the transport cost to anywhere west of Springfield is $0.4 per mile. Given the poor state of the roads through the mountains. the transport costs to anywhere east of Springfield is $0.8 per mile. (a) (1 point) Graph the costs of widgets produced throughout the entire 150-mile region. Carefully label the costs at the factory, at the far western end of the region, and at the far eastern end of the region (b) (1 point) Assume that the cost of making a widget at home is $44. What is the market area for the factory? (That is, how many miles west of Springfield will it stretch, and how many miles east of Springfield will it stretch?)EC330 PS01 Due Thursday October 14th - Page 7 of 11 Su2021 In reality, one of the key inputs for widgets is easier for the residents of the western plains to acquire. For all remaining parts of the problem, assume that the cost of making widgets at home anywhere west of Springfield is actually $32, and the cost of making widgets at home is $44 anywhere east of Springfield. (c) (1 point) Now what is the market area for the factory? (That is, how many miles west of Springfield will it stretch, and how many miles east of Springfield will it stretch?) Show your work. The owners of the factory would like its market area to extend more broadly, and they are considering two investment options: . First, they could help the government of the region finance the upgrading and paving of the mountain roads, which would reduce the transport costs east of Springfield to only $0.6 per mile. (The transportation costs west of Springfield would stay at $0.4 per mile.) Second, they could purchase and install expensive new equipment in the factory that would reduce the cost of a widget at the factory door to only $14 per unit. Each of these options would cost exactly the same, and the owners of the factory can choose only one of these options. Assume that potential customers for widgets are distributed evenly across the entire 150-mile region.(d) (1 point) How many additional miles (on either side of Springfield ) would be added to the factory's market area under the first investment option of upgrading and paving the mountain roads? Show your work. (e) (1 point) How many additional miles (on either side of Springfield ) would be added to the factory's market area under the second investment option of installing new equipment in the factory? Show your work. (f) (1 point) Given the answers to parts d) and e) above, which investment option will the factory owners choose? Briefly explain why they will go with that option