Two hotels are considering a location along a newly constructed highway through the desert. The highway is 500 km long with an exit every 50 km (including both ends). The hotels may choose to locate at any exit. These will be the only hotels for any traveler using the highway. Each traveler has their own most preferred location along the highway (at some exit) for a hotel, and will choose to go to the hotel closest to that location.Travelers’ most preferred locations are distributed evenly, so that each exit has the same number of travelers who prefer that exit. If both hotels are at the same distance form a traveler’s preferred location, then that traveler flips a coin to determine which hotel to stay at. A hotel would each like to maximize the number of travelers who stay at it

Which pairs of locations form Nash equilibria?

(This is a 3 part question but we have 1 question per so the other two was If Hotel 1 locates at the 100 km exit, where should Hotel 2 locate? Given Hotel 2’s location you just found, where would Hotel 1 prefer to locate? i also post other two so if you answer only this one it will very much appreciated )

Financial statement information is presented below for Hillary Corporation, a producer of mountain climbing gear. The company expects sales to increase by about 20% in 2004.

Hillary’s management is considering automating much of the company’s production process. The automation would result in about half of the company’s cost of goods sold being fixed. Currently, most of these costs vary in proportion to sales, as shown in the financial numbers presented above.

Required

A. Assume that half ($231 million) of Hillary’s cost of goods sold in 2003 is fixed and that the other half increases in proportion to sales, an increase of 20%. Compute the company’s expected cost of goods sold.

B. Using the same assumptions as part A, compute expected net income for 2004. Assume that income taxes are 35% of pretax income. Round to the nearest million.

C. Compare your results with those presented above, which assume that cost of goods sold varies in proportion to sales. What effect would the automation have on Hillary’s profitability? What effect would it have on the company’s risk? Explain your answer.