1. The following time-series plot depicts total fall enrollment at UGA from 1999 to 2007. Discuss whether it is appropriate to use moving average, weighted moving average, or simple exponential smoothing methods to predict future enrollment at UGA and why .
   
2. A linear trendline is added to the enrollment data using year as the independent variable with 1999 coded as year 1, 2000 as year 2, etc. The regression with coefficient estimates rounded to a whole number is as follows:
   y = 13715 + 363 t
   where y is the enrollment and t = 1, 2, 3, … is the year number. Predict the fall enrollment for 2008 and 2009.
3. Interpret the slope coefficient reported in part 2).
4. The UGA magazine reported that the university plans to reach a targeted enrollment of 25,000 by the year of 2015. Discuss if this goal is realistic based upon the regression estimate in part 2).
5. As the university continues to grow, Athens (The town UGA is located in) has recently seen the completion of two new hotels along the 301 bypass. Studies find that hotel occupancy rate is highly seasonal. Can you speculate on the seasonal patterns of hotel occupancy rate in Statesboro (a college town with a reputed football program) if quarterly data is available? Explain why your speculation is reasonable.
6. For 2006 and 2007, let’s assume that quarterly hotel revenues (in millions of dollars) in Athens were:

Q1 Q2 Q3 Q4

2006 8 9 12 7

2007 10 11.5 14 9

Use an appropriate method to estimate the trend and seasonality in this data and forecast the quarterly revenues accordingly for 2008. Attach supporting excel work on separate document.

Problem 2 (12 Points): Linear Programming

Galaxy II makes two popular strollers, LightGo and Smoothride. LightGo can be easily carried and Smoothride is heavier with large wheels. The company has been successful at selling both products for the last two years and wants to revisit its weekly production plan in light of the recent turbulence on the raw materials input market. The company estimates that a LightGo stroller will make $15 in profit and a Smoothride will make $40 in profit. For the next week, there are outstanding orders of 100 LightGo and 100 Smoothride that must be made to keep its most valuable customers happy. The inventory records of the company show that there will be 4,800 yards of steel bar available to be cut and used to assemble the frame of both strollers and there will be a total of 1,200 man hours for making both strollers. The company believes that it has plenty of other less critical resources for next week’s production. Each LightGo uses 6 yards of steel bar and 1 man hour to make and each Smoothride needs 8 yards of steel bar and 4 man hours to make. The company is looking to use an optimization model to determine its profit-maximizing plan for the next week.

1. (1) Write down a concise verbal model that articulates the objective, decisions, and constraints facing Galaxy II
2. (1) Spell out the decision variables involved
   X ₁ :
   X ₂ :
3. (1) Use the decision variables define in part b) to formulate a mathematical representation of Galaxy II’s production planning problem
   Objective: Maximize Profit =
   Subject to constraints:
   Constraint 1:
   
   Constraint 2:
   Constraint 3:
   
   Constraint 4:
   Constraint 5:
   
4. (2) Interpret each line of the mathematical formulation. Simply paraphrasing the equations will not earn any credit. An example of paraphrasing may be "4 times the number of LightGo plus 4 times the number of SmoothRide is less than or equal to 500." A business interpretation will state instead "The number of wheels used to make both products in the next week must be within the limit of 500 available wheels in inventory."
5. (2) Plot the constraints of the problem and identify the feasible region below
6. (1) Enumerate all the corner (or extreme) Answers corresponding to the feasible region you identified from part e) and determine the optimal production plan you recommend.

   Corner x-y coordinates	Profit

7. (1) Summarize the optimal Answer including the decisions, optimal profit, and implications of your constraints.
8. (3) Set up a Solver model to verify your graphical Answer found in the above and submit your Excel on a separate sheet.

Problem 3 (6 points): Decision Analysis

Tom inherited $1,000 and has hired a broker to help him decide where to invest this money. Tom has narrowed down his choices to bond, stock and CD account. Depending on the macroeconomic conditions classified into recession, expansion, and no significant change, the broker has estimated the returns of Tom’s investment options. The following table summarizes this information that the broker made available to Tom:

Expansion No Change Expansion

Bond $220 $160 -$110

Stock $270 $180 -$210

CD account $70 $70 $70

1. (1) If Tom is an optimistic investor, what investment option will he likely pick? Explain the rationale behind his decision.
2. (1) If Tom is a pessimistic investor, what investment option will he likely pick? Explain the rationale behind his decision.
3. (1) The broker has also informed Tom that economic conditions of recession and expansion are equally likely, and no major change is twice likely as recession. Calculate the probabilities associated with the three economic conditions.
   P(Recession) =
   P(Expansion) =
   P(No Change) =
   Show work here:
4. (1) If Tom uses the expected payoff to make his investment decisions, what investment will he pick? Support your result with appropriate work.
5. (2) Determine the expected value of perfect information for Tom and explain to him how this value might be useful to him.

Price: $27.38

Solution: The downloadable solution consists of 13 pages, 1438 words and 2 charts.
Deliverable: Word Document