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2. End of Line The city of Frisco lies at the western end of a rail line. To the east are a hundred miles of wide plains along which there are several towns-all connected to Frisco by the rail line. To the west of Frisco are fifty miles of mountains, whose small villages are connected by a few winding dirt roads. The only factory in the region is in Frisco. It produces widgets at a cost of $20 per unit at the factory door. Thanks to the mountains, the transport costs to anywhere west of Frisco is $0.50 per mile a. 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. Cost (in S) - west Frisco east b. Assume that the cost of making a widget at home is $28. What is the market area for the factory? That is, hovw many miles west of Fisco will it stretch and how many miles east of Frisco mllit stretch) Showrour поп.In reality, one of the key inputs for widgets is easier for the residents of the eastern plains to acquire. For all remaining parts of the problem, assume that the cost of making widgets at home anywhere east of Frisco is actually $26, and the cost of making widgets at home is $30 anywhere west of Frisco. c. Now what is the market area for the factory? (That is, how many miles west of Frisco will it stretch, and how many miles east of Frisco will it stretch?) Show your wor number of miles to the west of Frisco number of miles to the east of Frisco 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 inance the upgrading and paving of the mountain roads, which would reduce the transport costs west of Frisco to only $0.40 per mile. (The transportation costs east of Frisco would stay at $0.10 per mile.) Second, they could purchase and install in expensive new equipment in the factory that would reduce the cost of a widget at the factory door to only $10 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. How many additional miles (on either side of Frisco) would be added to the factorys market area under the first investment option of upgrading and paving the mountain roads? Show your work.e. How many additional miles (on either side of Frisco) would be added to the factorys market area under the second investment option of installing new equipment in the factor? Show your work miles added to the factorys market are:a f Given the answers to parts d) and e) above, which inrestment option will the factory owners choose? Briefly explain why they will go with that option.

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Solution! A toin rail line is loid in α series or 20 m lengths sepayated on each Side Some gap iven data HD BCO | 46mm. H6q8 mm FD HD43 3mm Buu 24.6 x 633 2 x333.3 x 6.34 9y 12 626 mn (200oo)39-632 k A E Sap a 3.8 mm Gap 8.8 mm The minimum gap lergh vequired 882 m

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