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Southwestern University (SWU), a large state college in Stephenville. Texas, enrolls close to 20,000 students. The school is a dominant force in the small city, with more students during fall and spring than permanent residents.

Always a football powerhouse, SWU is usually in the top 20 in college football rankings. Since the legendary Phil Flamm was hired as its head coach in 2009 (in hopes of reaching the elusive number 1 ranking), attendance at the five Saturday home games each year increased. Prior to Flamm's arrival, attendance generally averaged 25,000 to 29,000 per game. Season ticket sales bumped up by 10,000 just with the announcement of the new coach's arrival. Stephenville and SWU were ready to move to the big time!

The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in 1953, has seating for 54,000 fans. The following table indicates attendance at each game for the past 6 years.

One of Flamm's demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head-on. Flamm had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.

SWU's president, Dr. Joel Wisner, decided it was time for his vice president of development to forecast when the existing stadium would "max out." The expansion was, in his mind, a given. But Wisner needed to know how long he could wait. He also sought a revenue projection, assuming an average ticket price of S50S 50 in 2016 and a 5%5 \% increase each year in future prices.

2010 2011 2012
1 34,20034,200 Rice 36,10036,100 Miami 35,90035,900 USC
2a^a 39,80039,800 Texas 40,20040,200 Nebraska 46,50046,500 Texas Tech
3 38,20038,200 Duke 39,10039,100 Ohio State 43,10043,100 Alaska
4b4^b 26,90026,900 Arkansas 25,30025,300 Nevada 27,90027,900 Arizona
5 35,10035,100 TCU 36,20036,200 Boise State 39,20039,200 Baylor
2013 2014 2015
1 41,90041,900 Arkansas 42,50042,500 Indiana 46,90046,900 LSU
2a^a 46,10046,100 Missouri 48,20048,200 North Texas 50,10050,100 Texas
3 43,90043,900 Florida 44,20044,200 Texas A8M 45,90045,900 South Florida
4b^b 30,10030,100 Central Florida 33,90033,900 Southern 36,30036,300 Montana
5 40,50040,500 LSU 4,8004,800 Oklahoma 49,90049,900 Arizona State

a^a Homecoming games. b^b During the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance.

Discuss the school's options.

With the growth of Hard Rock Cafe - from one pub in London in 1971 to more than 145 restaurants in 60 countries today-came a corporatewide demand for better forecasting. Hard Rock uses long-range forecasting in setting a capacity plan and intermediate-term forecasting for locking in contracts for leather goods (used in jackets) and for such food items as beef, chicken, and pork. Its short-term sales forecasts are conducted each month, by cafe, and then aggregated for a headquarters view.

The heart of the sales forecasting system is the point-of-sale (POS) system, which, in effect, captures transaction data on nearly every person who walks through a cafe's door. The sale of each entrée represents one customer; the entrée sales data are transmitted daily to the Orlando corporate headquarters' database. There, the financial team, headed by Todd Lindsey, begins the forecast process. Lindsey forecasts monthly guest counts, retail sales, banquet sales, and concert sales (if applicable) at each cafe. The general managers of individual cafes tap into the same database to prepare a daily forecast for their sites. A cafe manager pulls up prior years' sales for that day, adding information from the local Chamber of Commerce or Tourist Board on upcoming events such as a major convention, sporting event, or concert in the city where the cafe is located. The daily forecast is further broken into hourly sales, which drives employee scheduling. An hourly forecast of $5,500\$ 5,500 in sales translates into 19 workstations, which are further broken down into a specific number of waitstaff, hosts, bartenders, and kitchen staff. Computerized scheduling software plugs in people based on their availability. Variances between forecast and actual sales are then examined to see why errors occurred. Hard Rock doesn't limit its use of forecasting tools to sales. To evaluate managers and set bonuses, a 3-year weighted moving average is applied to cafe sales. If cafe general managers exceed their targets, a bonus is computed. Todd Lindsey, at corporate headquarters, applies weights of 40%40 \% to the most recent year's sales, 40%40 \% to the year before, and 20%20 \% to sales 2 years ago in reaching his moving average.

An even more sophisticated application of statistics is found in Hard Rock's menu planning. Using multiple regression, managers can compute the impact on demand of other menu items if the price of one item is changed. For example, if the price of a cheeseburger increases from $7.99\$ 7.99 to $8.99\$ 8.99. Hard Rock can predict the effect this will have on sales of chicken sandwiches, pork sandwiches, and salads. Managers do the same analysis on menu placement, with the center section driving higher sales volumes. When an item such as a hamburger is moved off the center to one of the side flaps, the corresponding effect on related items, say french fries, is determined.

MONTH 1 2 3 4 5 6 7 8 9 10
Guest count (in thousands) 21 24 27 32 29 37 43 43 54 66
Advertising (in S thousand) 14 17 25 25 35 35 45 50 60 60

What is the role of the POS system in forecasting at Hard Rock?


When applying LP to diet problems, the objective function is usually designed to:

a) maximize profits from blends of nutrients.

b) maximize ingredient blends.

c) minimize production losses.

d) maximize the number of products to be produced.

e) minimize the costs of nutrient blends.


Answered 12 months ago
Answered 12 months ago
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In this problem, we are asked to determine the correct answer in determining the objective function of diet problems in linear programming.

Let us start analyzing each given alternative and identify the correct answer.

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