MAT 117

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Theme Park Log

MAT117 Project

Submitted by: _____________________________________ Date: ________________

Instructions (read carefully before beginning)

This project places you in the position of managing a recreational water theme park that is open for 12 weeks in the summer.

As Director of Operations you oversee all aspects of the park from grounds keeping to facilities to financials. The Board of Directors requires you to keep a weekly planning and issues log which includes a description and detailed report of your management decisions.

The following is the list of the items in your log for your first week on the job. In this project you must complete each log entry. Each log entry must contain a description of the issue and an explanation of the steps you took to resolve the issue.

Try to use the space in this packet to do your work. However, if you need more space, please use Appendix A to attach additional work.

If you use Appendix A, be sure to clearly refer to the Appendix in each problem that has additional information in the appendix AND clearly label all work in the appendix.

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Park Power The park supplements its energy consumption by using a field of 300 solar panels. The maintenance team reports that in a recent storm 75 of the panels were damaged. You need to call the vendor for replacement panels but first you need to know the pricing model that was negotiated for the park. After digging through the files and looking at past receipts, you find the following information: the cost for buying 30 replacement panels was $3600 and the cost for buying 60 replacement panels was $5250 and this pricing model is valid for up to 100 panels. Using this information, do the following:

1. Create a model for the board to use to determine the cost of buying panels. Model: ___________________________

2. provide a description of the variables in your model and instructions to the board of how to use the model:

3. Use the model to determine the cost to replace the damaged panels? Cost for 75 panels: _________________________

4. It seems there is a fixed cost just to place an order, what is this cost? _______________

5. What is the cost per panel? ____________________

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Park Power Work and Explanations:

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Medical Transport Plan The board of directors is preparing a report regarding the relationship the park has with the nearest medical facilities. There is a medical clinic in a nearby city that will take emergency patients and then can medivac the patient by helicopter to the nearest hospital. The average speed of an ambulance to the clinic is 60 mph. The average speed of the medivac helicopter traveling from the clinic to the hospital is 150 mph. From the time the patient is loaded into the ambulance they can be at the hospital in 2.5 hours. The entire distance is 240 miles. Find:

1. the distance from the park to the clinic: _________________miles

2. the time it takes the ambulance to go from the park to the clinic: _______________hours

3. the distance from the clinic to the hospital: ____________________miles

4. the time it takes for the helicopter to go from the clinic to the hospital: __________hours

Work and explanations:

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Food and Beverage Services The food stands plan to carry a new punch drink that has been requested by patrons. The punch uses orange juice and cranberry juice. A gallon of orange juice costs $2 and a gallon of cranberry juice costs $3.20.

1. How many gallons of each juice must be mixed to create 100 gallons of punch that costs $2.30 per gallon? Orange Juice: _________ Cranberry Juice:____________

2. What is the total cost to make 100 gallons of punch? ________________

3. What is the food stand’s cost for a 16 ounce serving? (round to the nearest hundredth) Cost of 16 ounce serving: ________________

4. The park plans to sell the punch for $1 per glass. What is the percentage markup? Markup percentage: ____________

Work and Explanations:

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Ride Management The park has a train ride that provides a tour of the park. A marketing firm has provided a study indicating that the ride should only last 60 minutes. The loop around the park is 12 miles long. If the first two-thirds of the trip is very scenic and should be traveled at 10 mph,

1. How many miles are traveled at 10 mph? ___________________________________

2. How much time, in minutes, is used up for the scenic portion of the trip? __________

3. How much time, in minutes, is left to return to the station? _____________________

4. At what rate must the train travel to have the train return on time? _______________ Work and Explanations:

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Grounds Keeping The grounds keeper would like to hire an apprentice for the summer. The lawns must be mowed once per week. If the grounds keeper can do all the lawns by himself in 6 hours, at what rate must the apprentice be able to do the lawns so that when they work together they complete the job in 4 hours? Rate of apprentice: _______________ Total Hours for apprentice to do all the lawns alone: _________________ Work and Explanations:

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Depreciation of Equipment Three years ago the maintenance department purchased a zero turn lawnmower for $5000. It is now valued at $3200. Construct a linear model for the depreciation of the lawnmower. How much will the lawn mower be worth after one more year of use? Model: ____________________________________________________ Value: ____________________________________________________ Work and Explanations:

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New Merchandise Sales Goal The park sells souvenir t-shirts. It costs $10 per shirt plus an initial $1200 processing fee to set up for the design to be printed on the shirt. The park sells the t-shirts for $15.25. How many t- shirts must be sold to break even? How many must be sold to earn a profit of $10,000? Cost Function: ___________________________ Revenue Function: ________________________ Profit Function: __________________________ Quantity Required to earn a profit of $10,000: ____________________ Work and Explanations:

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Change in Souvenir Pricing The park sells souvenir reusable bags. The park maintains that it works to keep costs down for its customers and has dropped the price of the bag by 15%. The bag now costs $8.50. What did it cost last summer? Last summer’s price: _________________ Work and Explanations:

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Merchandise Pricing - Camera

The number x of digital cameras the park is willing to sell is given by x = 25p - 500, where p is the price, in dollars, per digital camera. The number x of digital cameras patrons are willing to purchase is given by x = - 7p + 1100, where p is the price per digital camera. Find the equilibrium quantity and price.

Equilibrium Quantity: _________________________ Equilibrium Price: ____________________________ Work and Explanations:

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Roller Coaster Height and Drop The marketing team wants to publish some information about the parks roller coaster in a brochure. They have the following equation and diagram but do not know how to calculate the information they need for their brochure. They would like to publish the

ℎ 𝑡 = .5𝑡& − 4𝑡 + 500 where h is the height in meters and t is the time in seconds. Find the height of the roller coaster above the ground before it drops: ________________ Beginning at the “Top”, how many meters does the roller coaster drop when it reaches the location marked “Bottom of Drop” (see the black arrows on the diagram)? _________________ How long does the drop take? _______________

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Roller Coaster Work and Explanations:

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Attendance Forecast You know that weekly attendance is related to the temperature. You have the following data from the prior summer regarding average weekly temperature and attendance. To order the appropriate supplies for the vendors in the park for each week you need to use the weather forecast to predict the attendance. Given the data above, create a linear regression model to predict the attendance for your second week. Your weather analyst forecasts the average temperature to be 76 degrees. Linear Model: ___________________________________________ Predicted Attendance for Week 2: ____________________________ What is the slope of the model? _____________________________ Interpret the slope: _____________________________________________________________ Work and Explanations:

Week # Average weekly temperature (Fahrenheit)

Attendance for that week (Thousands)

1 65 1 2 67 1.5 3 63 .5 4 72 1.5 5 77 2.5 6 75 2 7 79 2.75 8 85 3.5 9 83 3 10 84 3 11 87 5 12 85 4

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Bacteria in the Restrooms A species of bacteria is found in a restroom at 6 a.m. with a population of 250 thousand. The population growth rate is represented by:

𝑃 𝑡 = 250( 2 / & )

where P is the population and t is time in hours. Determine the population at 9 p.m. if the cleaning crew does not disinfect the restroom. Bacteria Population at 9 PM: _______________________________________ Work and Explanations:

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Appendix A – Additional Work and Supporting Materials