Who do you think is correct, Mark (the unload capacity should be twice as high) or Doug (the two lifts have the same capacity)? Can you give a response to Jessica—is there any other difference between the two lifts? 

Those of you who are skiers or snowboarders know that some resorts have “high-speed” chair lifts. These lifts are called “detachable” because the chair detaches from the main cable just before loading people. Once the passengers are “on board,” the chair reattaches to the main cable and “rockets” to the top at a much faster speed than the traditional “fixed-grip” counterparts that remain firmly attached to the main cable. 

Cougar Mountain, a medium-sized and profitable ski resort, currently has a traditional fixed-grip quad lift that takes guests from the main lodge at the bottom of the mountain up to the peak. While it prides itself on the quality of its terrain and friendly service, Cougar Mountain’s owner, Jessica Powder, is concerned that the traditional (a.k.a., slow) lift will start to deter its established guests from returning year after year. It is time for it to consider replacing the traditional lift with a high-speed quad. 

Jessica asked her chief operating officer, Doug Bowl, to collect some data on the current lift and the proposed new one. Once he had the data, listed in Table 2.7, he met with Jessica and Mark Ketting, who is responsible for Cougar’s sales and advertising 

Mark immediately started the conversation by saying, “Customers are going to love that their ride time will be cut in half by the new lift. But there must be a mistake in Doug’s data. If the new lift doubles the speed at which skiers travel up the mountain, then it must be that it can unload more skiers at the top at a faster rate! Shouldn’t the unloading capacity double?” Doug responded, “I think the table is correct because from what I have observed, people are not able to load onto a detachable lift any faster than on a fixed-grip lift.” Jessica jumped in, “Doug, assuming you are right, and I am not sure you are, does that mean the only difference between a fixed-grip and a detachable lift is that one moves faster than the other?” 

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TABLE 2.7 Performance Data for the Current Fixed-Grip Quad Lift and a Proposed Detachable Quad Lift at Cougar Mountain Fixed-Grip Detachable Length of lift (meters) 700 700 Passengers per chair 4 4 Time from bottom to top (sec) 250 125 Unloading capacity (skiers per hour) 2400 2400