Winter is fast approaching and it is finally time to hit the slopes! With the upcoming 2018 Winter Olympics in

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1 Team 7410 HiMCM Page 1 of 17 Summary: Winter is fast approaching and it is finally time to hit the slopes! With the upcoming 2018 Winter Olympics in mind, investors are looking to develop a new high-end ski resort in the state of Utah. Our group was tasked to design the layout for a ski resort at the Wasatch Peaks Ranch. We are also looking to see if this venue could be considered as a candidate to host the 2026 Winter Olympics. To help with our investigation, we were provided with a topographic map of the area and a set of data points of other North American resorts and international ski resorts that will host / have hosted the Winter Olympics. The investors had some specifications that they wanted us to include in the design. For example, the distribution of slopes was limited so that 20% of the slopes were beginners trails whereas the intermediate and advanced trails comprised 80% of the slope (40% intermediate and 40% advanced). The total distance of all the trails combined had to at least exceed 160 km and they had to be varied in lengths. Our group approached the investors request with 2 different design layouts. Our first design focused on maximizing options so that athletic / competitive skiers could practice in the same difficulty regions while taking different paths. The second method comprised of trails in the shape of a loop. This allowed for exposure to various scenic views and introduced a range of obstacles (uphills and curbs) to build stamina. In order to evaluate the best design for the resort, three decision matrices were used. The original intent was to run the data through statistical analyses, however the lack of a proper sample size prohibited the use of these tests. The advantageous property of using a decision matrix allows a multitude of criteria to be analyzed at once. This way, critical requirements are weighted with higher value than lesser criteria to establish importance. In our comparison of the two designs, Design One scored a higher value on the matrix because it had better placed lifts, appealed more to a wider range of sports, and overall had a simpler layout than Design Two. According to the results of our Olympics evaluation matrix, it can be determined that Design One is more suitable to host the Winter Olympics and serve as a recreational setting for the general public. However, if the investors were looking to build this resort solely for athletic skiers, Design Two would be more favorable due to the convertibility of the beginner course as a long distance cross country skiing and stamina training course.

2 Team 7410 HiMCM Page 2 of 17 Memo: Dear Ms. Mogul, We have thought long and hard about possible layouts of ski trails for Wasatch Peaks Ranch, and have created two layout designs that would suit your needs. Both of the trails meet the criteria required to develop the area into a first-class venue, but differ in appeal to its guests. The first of the designs aims to attract athletes practicing for a variety of events. These events are mainly alpine downhill and slaloms, cross-country, ski jumping, snowboarding and freestyle skiing. However, these trails can be easily converted to suit other events. Design One features a 0.44-kilometer range of elevation, with 208 total kilometers of trails that follow the preferred layout of having twenty percent of the trails being beginner level, forty percent intermediate level, and forty percent advanced level. To ensure that guests can travel through the venue both easily and comfortably, the plan includes the construction of twenty lifts. The second design intends to attract athletes competing in all the events that Design One accounts for, except cross country skiing, and can host an additional event of Nordic skiing. Like the other design, though, these trails can also be easily adapted for other events. This plan features a 0.44-kilometer range of elevation, with 164 total kilometers of trails set in large looped paths that allow for stamina training in addition to the events listed. Twenty-one lifts will be needed to insure comfortable transportation. If there is a stronger intent to create a venue suitable for guests of all backgrounds, the first method would be preferred. The design has many slopes for beginners to train on while still presenting intermediate and advanced skiers with ample space. If the desire is to have a venue truly suitable for Olympic activity, Design Two would be preferred. While the first plan is satisfactory, the second was designed to allow skiers to practice for the events and train for their stamina as well. Moreover, the beginner course of this design is incredibly fit for both cross-country skiing and stamina training. We realize that only one of these designs can be constructed, so we leave the decision for you to make based on which plan better fits your needs. Lodging and safety is also a very important aspect of a ski resort. In order to make the facilities of the resort accessible to guests, we decided that there should be two lodges and two cabins placed in strategic

3 Team 7410 HiMCM Page 3 of 17 locations along the trails. The lodges lie on the northern and southern ends of the property and will have all of a guests necessities. Cabins will be positioned on the north-western and south-eastern sides, and will contain bathrooms, a phone, warm attire, preserved food, and first aid kits for emergency situations. As the land was analyzed, our team also came to the conclusion that the resort would not be accessible by guests. Though there is a highway neighboring the property, creeks along the road make it impossible for guests to enter the resort. To resolve this complication, there would have to be bridges that connect the road to the property with a highway exit and main entrance. We hope that you are satisfied with the layouts that were created for the resort. Our team worked hard to create designs that, according to the criteria, would be better than the average venues both in North America and those to be used for the Winter Olympics. We look forward to working with you again. Sincerely, Team 7410

4 Team 7410 HiMCM Page 4 of 17 Introduction: Problem: A group of wealthy winter sports fans are interested in developing a high end ski resort, and Wasatch Peaks Ranch in Peterson, Utah, USA is available for sale. Our team was called to investigate and identify potential ski slopes and trails on the property in order to develop the mountain as one of the top ski resorts in North America. Additionally, the investors hope that the layout will serve as a potential candidate to host the future 2026 Winter Olympics. To determine whether this plot of land will be suitable for this resort and the Olympic arena, we were asked to rank our proposed ski area against existing ones in North America. Given Area: Wasatch Peak Ranch, listed at thirty-nine million dollars, occupies 20 square miles of natural alpines with a total of 13,000 deeded acres of which 5,500 holds the potential to be ski slopes. The land also contains an 11-mile ridge line including 24 peaks and 15 bowls. With highest elevations at around 9,570 feet and lowest at 4,820 feet, the land offers a wide range of different slopes and elevations. Its close proximity to Salt Lake City and Salt Lake International Airport (a mere 35 minutes) maximizes the accessibility to local skiers as well as travelers. The area accumulates 400+ inches in snowfall annually, providing a suitable environment for skiers in the winter season.

5 Team 7410 HiMCM Page 5 of 17 Figure 1. This given map was also used very frequently while completing the problem. Design Requirements: 1. Main slopes must be of varying lengths 2. There need to be plenty of trails. 3. There must be a total of at least 160 km of slopes (main slopes and trails). 4. Distribution of slopes at approximately 20% rated beginner ( green circle), 40% rated intermediate ( blue square), and 40% rated difficult ( black diamond). Assumptions: 1. This land will be purchased regardless of whether the resort can suit the requirements to host the Olympics or not. 2. The slopes will be distributed so that 20% will be beginner trails, 40% will be intermediate trails, and 40% will be advanced trails.

6 Team 7410 HiMCM Page 6 of To classify as an advanced slope, at least one part of the trails must fall within the designated advanced area. The same will be said for beginner trails and intermediate trails. 4. Any stretches of trails that overlap with other difficulty levels will be treated independently, e.g. the length of trails that are shared between both intermediate and advanced levels will be added to the total length of both levels. 5. Due to the lack of budget information, it is assumed that these investors are willing to pay the necessary expenses to meet and potentially exceed all of the minimum requirements. 6. Due to the number of creeks and rivers in the area, it will be assumed that the land is stable enough to support bridges to allows for maximum accessibility to the resort and its features. 7. Once the resort approaches completion, the investors have the means to obtain permits and create an exit off of highway 31 that will lead to the main entrance of the resort. 8. The resort will remain open year round to maximize revenue. 9. All trails, lodges, cabins, and services will be maintained regularly by staff. Strategy: Initial View: The initial strategy was to create two plans: one design that met basic criteria and minimum requirements, and another that exceeded these specifications. The design that exceeds the criteria would account for real life situations such as transportation between slopes and trails, customer comfortability, and easy accessibility. Revision: After continuously brainstorming potential situations, it was decided that a more optimal strategy would be to provide the investors with two separate designs. These designs would contain a different layout of trails while still remaining in the designated difficulty regions. They would both have the extra features that would exceed the criteria (e.g. the efficient transportation methods). Before continuing and developing our trail designs, we created three decision matrices. These matrices contained all of the necessary criteria that the investors are looking for.

7 Team 7410 HiMCM Page 7 of 17 Finding the Slopes / Dividing Regions: The elevation and terrain distance measurements were found and taken from Google Earth. The contour lines on the given map were analyzed to determine the general elevation of specific regions. Based on the general elevation in each regions, we categorized them based on their expected difficulty level: beginner, intermediate, and advance. The slope of the trails were found by taking the elevation of each trail and dividing it by the total distance. The elevation of each trail (above sea level) was found by subtracting the ending point from the starting point. Total distance for each trail was found by measuring the entire pathway from the starting location to the final location. Figure 2.1. Slopes and Dividing Regions. Points. Figure 2.2. Slopes and Dividing Regions. Regions.

8 Team 7410 HiMCM Page 8 of 17 Table 1. Finding the Slopes of Each Area Area Low elevation Finding the Slopes of Each Area High Elevation Rise (ft) Rise (mi) Run (mi) Slope Beginner's Beginner's Intermediate Intermediate Intermediate Advanced Advanced Methods: After calculating the different slope regions, our team worked on trail placement. While working on this, it was important to keep in mind the suggested slope distributions (20% beginner, 40% intermediate, and 40% advanced) and the minimum total trail length requirement (160 km). It was decided that the optimal length of the beginner path would be 20 miles (approximately 32 km), and the intermediate and advanced paths would both be 40 miles (approximately 64 km each). This would give a total of 100 miles (approximately 160 km). Method 1: The basic layout of Method One displays common points at the bases of different inclines and branches sub-trails in multiple directions. The purpose of these trails were so that skiers could ski to the top of the incline and ski back down the same way they came from. The objective of this layout was to maximize the number of options skiers can take while still being in the same region of their difficulty level. It also allows any people who are practicing for various events, therefore enabling them to explore the same region through different paths. Another point in Method One was to create more options for skiers to either take long scenic / cross country skiing routes, straightforward routes, or take a lift directly to their destination. To achieve this, our team

9 Team 7410 HiMCM Page 9 of 17 created multiple forks along trails that would run along higher slopes. If skiers choose not to ski up to the top of a slope, they can change direction and head towards the cabins or lodges. Figure 2.1. Method 1. Figure 2.2. Method 1 lifts. Method 2: For the second approach, our team took a more systematic process. The trails were distributed based on the difficulty level of the region. Each trail began from a designated point and followed a loop-like path back to the start point in order to maximize trail length. The advantages of using the loop trails included exposing the skiers to various scenic views, introducing a range of obstacles (uphills and curbs), and building stamina. The layout of the trail was designed strategically to allow the skiers to continue in a moving motion without coming to a sudden halt. The total distance for each trail, based on difficulty level, was recorded.

10 Team 7410 HiMCM Page 10 of 17 Figure 3.1. Method 2. Advanced paths. The black trail goes through advanced region 1. The brown trail goes through advanced region 2 Figure 3.2. Method 2. Advanced paths with lifts. Figure 3.3. Method 2. Intermediate paths. The light blue trail goes through intermediate region 3. The dark blue trail goes through intermediate region 2. The purple trail goes through intermediate region 1. Figure 3.4. Method 2. Intermediate paths with lifts.

11 Team 7410 HiMCM Page 11 of 17 Figure 3.5. Method 2. Beginner path. The green trail goes through beginner region 1. Figure 3.6. Method 2. Beginner path with lifts. Results: After creating our two designs, we calculated the statistics in regards to the categories that were given in the original Excel files. Table 2. Statistics on Our Models Our Plans Category Plan 1 Plan 2 Category Plan 1 Plan 2 Peak Elevation (m) % Green Base Elevation (m) Blue Range of Elevation % Blue Skiable Acres Black Slopes Total % Black % Slopes to Skiable Acres Green Lifts Amount of Trail per Lift

12 Team 7410 HiMCM Page 12 of 17 The original plan was to analyze the data with a statistical analysis test such as a two-proportion Z-test but, due to the lack of proper sample sizes for each group, the assumptions for the Z test (e.g. np and nq have to be greater than 10) could not have been met. Consequently, we decided to use a new approach to analyze the data through a decision matrix. The results from the decision matrix would determine whether our designs were better than the data given from the Excel sheet (North American Ski Resorts list and Winter Olympic Venue list). Ranking System: Our team created three decision matrices: one reviewing our plans for the trails, another comparing our plans to other North American resorts, and a final one comparing our plans to past Olympic Venues. Each decision matrix had its own criteria specific to the needs of the situation. In weighting system of the matrix used to decide the most appealing method (Table 2), each criterion could receive a score of a three, a six, or a nine, with three being the lowest score, six being the next highest score, and nine being the highest score a criterion can receive. The scores were totaled and divided by the number of points available to create a final score for plan one and plan two. The weighting system of the matrices comparing our design to those of other North American resorts and Olympic venues was different. These matrices used the averages of the other data sets given for each category as a standard. Each criterion for our plans could be ranked a -1, 0, or 1, depending on how they were designed in accordance to that criterion. If a plan suited the criterion better than an average stadium, it would get a 1, if it preformed the same, it would receive a 0, and if it preformed worse than the existing stadiums, it would receive a -1. After the ranking, the scores were summed to a value would indicate and overall better design if positive.

13 Team 7410 HiMCM Page 13 of 17 Data Analysis: Part 1: Table 3. Decision Matrix to Decide the Best Plan Reviewing our Plans for Trails Criteria Weight Plan 1 Plan 2 1. Meets required trail distribution ( %) At least 160 km of tails Trails easily accessible from lodges and road Main slopes of varying length Accessible/well placed Lifts Strategically placed cabins/facilities for customer facilities Good use of space (trail covers entire property) Varied terrain (different types of trails) Appeals to those participating in large range of winter sport Simple Overall Design Total Score: Percentage: Plan 1 meets 94.7% of the criteria while plan 2 meets 91.3% of the criteria. Part 2: The following two tables compare the calculated data in Our Plans table to the North American Ski Resorts as well as the other international Olympic ski resort. The data shows that both of our beginners and advanced trails exceed the average North American Ski Resort trails while plan 1 has a higher amount of trails per lift value and plan 2 has a lower trail per lift value. In the comparison to the Olympic Ski Venues table, both our plans exceeded the percentage of intermediate and the advanced trails to the international ski resorts.

14 Team 7410 HiMCM Page 14 of 17 Table 4. Decision Matrix Comparing Our Plans to the Average North American Resort Criteria 1. Meets required trail distribution ( %) Comparing to Other North American Resorts Average Resort % Plan % Plan 1 Score -1 Plan % 2. At least 160 km of trails Large amount of lifts Large number of skiable acres 5. Large proportion of trails per skiable acre Plan 2 Score % 3.80% % High range of elevation Small proportion the amount of trail per lift Sum: 1 Sum: 3-1 Plan 2 ranked better than both plan 1 and the average North American resort with a sum of 3 while plan 1 had a sum of 1 Table 5. Decision Matrix Comparing Our Plans to the Average Olympic Venue Criteria 1. Meets required trail distribution ( %) Evaluating Against Current Olympic Venue Average Venue % Plan % Plan 1 Score -1 Plan % 2. High total slope length High range of elevation Large amount of lifts Plan 2 Score Small proportion the amount of trail per lift 6. Beginners slopes can be used for Olympics TRUE Possible 0 TRUE 1 Sum: 1 Sum: 1

15 Team 7410 HiMCM Page 15 of 17 Conclusion: Limitations: The statistical analysis was limited due to the lack of data from the Wasatch Mountain Peaks as well as data from the other ski resorts. Therefore, decision matrices were used to evaluate and interpret the results of the data. The data on the skiable acres for the international ski resorts that will host / have hosted the Olympics were excluded due to lack of information given from the data set. Future extensions: For future extensions on the project, different trails can be mapped out to maximize trail length within the given acreage (5,500 acres). More data could be collected on Wasatch Peak Ranch in order to run statistical tests and comparisons between this land and other North American ski venues could be made using ANOVA tests. Our strategy used to examine Wasatch Peak Ranch could evaluate any new potential ski venues and compare its ranking to other ski lodges in North America.

16 Team 7410 HiMCM Page 16 of 17 Works Cited: References Wasatch Peaks Ranch Mirr Ranch Group. (n.d.). Retrieved November 10, 2017, from MASTER PLAN PROPOSALS. (2011) Retrieved November 10, 2017, from Plan/September2011.pdf. Map of Wasatch Peak Ranch N and W. Google Earth. December November 10, 2017

17 Team 7410 HiMCM Page 17 of 17 Appendix: Tables of given data, our data, and averages. Name State Country Peak Elevation (m) Base Elevation (m) Range of Elevation North American Ski Resorts - Partial List Skiable Acres Slopes Total % Slopes to Skiable Acres Green % Green Blue % Blue Black % Black Lifts Beaver Creek Colorado USA Big Sky Resort Montana USA Breckenridge Colorado USA Breckenridge British Columbia Canada Jackson Hole Wyoming USA Killington Vermont USA Lake Louis Alberta Canada Park City Mountain Utah USA Silver Star British Columbia Canada Squaw Valley California USA Steamboat Springs Colorado USA Sugarloaf Mountain Maine USA Sun Peaks British Columbia Canada Vail Colorado USA Whistler Blackomb British Columbia Canada Winter Park Resort Colorado USA Averages Amount of Trail per Lift Name State Country Peak Elevation (m) Base Elevation (m) Range of Elevation Our Ski Trails at Wasatch Peaks Ranch Skiable Acres Slopes Total % Slopes to Skiable Acres Green % Green Blue % Blue Black % Black Lifts Wasatch Peaks Ranch Plan 1 Utah USA Wasatch Peaks Ranch Plan 2 Utah USA Amount of Trail per Lift Name City Country Peak Elevation (m) Base Elevation (m) Range of Elevation Skiable Acres Slopes Total Green % Green Blue % Blue Black % Black Lifts YongPong Alpine PyeongChang South Korea Ski Resort Jeongseon PyeongChang South Korea Rosa Khutor Sochi Russia * values for skiable acres were not given Winter Olympic Venues (2018, 2014) Averages Amount of Trail per Lift