Problem 1. Assume that you are the President of the Student Government Association at UNC Chapel Hill and that you attended a briefing on an upcoming Bond Referendum for new facilities at all UNC System Campuses.  The amount allocated to Chapel Hill is over $1,000,000,000.00.  In a fit of enthusiasm, you volunteered that the UNC SGA would print and assemble 80,000 yard signs urging voters to approve the Bond Referendum.   The signs are to be 24 inches high and 15 inches wide and are to be stapled to 1" x 1" wood stakes, which are 42" long and sharpened on one end. A(rich) UNC alum, who owns a large building supply business has volunteered to donate these stakes.  However, he wants you to organize transporting these to UNC from his facility in Durham. It is 10 miles from UNC.   The stakes come in bundles of 36, which weigh approximately 50 lbs each. The bundles of 36 stakes are 6" x 6" x 42" each.   The university has 4 trucks, which have Cargo Bodies, which are 18' long, 8' wide and 8' tall and are rated to carry 20,000 pounds of cargo. They are available to the SGA for a rental of $50.00 per 24 hour day, plus gasoline.   You estimate that a crew of 4 UNC football players (The FB coach volunteered the team) can load 480 bundles per hour, but need a 10 minute break every hour, plus an hour for pizza and coke after every four hours. The print shop has just told you that they can print the signs on heavy paste board for $0.25 each, and need 2 hours to set up the press and then can print 8000/hr.   They work 8 hour days.  No overtime.   You will have to organize teams of students to staple the printed signs to the stakes and package them into bundles of 50 to be picked up by the NC Democratic Party.   You have contacted Lowe's and found out that you can purchase electric staple guns for $50 each and can get ½" staples for the guns for $4/1000 staples.  UNC has 4' x 12' tables and plenty of extension cords. You need to develop an estimated budget for this bright idea, a tentative schedule, and some idea of how many student volunteers you will need.  You must also budget for the pizza and soft drinks needed to feed the volunteers.  Also you owe a call to the head of the NC Democrats to tell him how long it will be until you can have the yard signs ready for pickup.  

a.          Develop a process for assembling the yard sign.  Assume that you use 1 stake, one pasteboard sign and staple three staples per sign.  Estimate how you will organize the work, how big a single team will be, how many signs per hour to plan for, how many staple guns you need to rent, and how many tables 4' x 12') you will need.  Also estimate how big a space you will need to work in.  Sketch a possible layout of the work area and indicate where the stakes and printed sign supplies are to be stacked and where the finished yard signs will be stacked.

b.      Develop a schedule, including picking up the stakes, printing the signs and assembling them.  Present this schedule as a Gannt Chart

c.       When should you be through, if you start March 15?

d.      How many football players do you need to load the N trucks (determine what N should be)?  How long will they work?

e.       Develop a budget estimate for this effort.  State assumptions you must make (i.e. pizzas/volunteer; soft drinks/volunteer/day; cost of pizza, cost of soft-drink 12 pack, etc)

f.       Should you keep your big mouth closed in the future?

Problem 2. You own a group of convenience stores in North Carolina and are interested in developing a forecasting model to use in predicting the average daily sales of a given convenience store to guide future purchases or construction of additional stores.  You have collected the following data on your current stores:

1. What factors should be used in forecasting daily sales and WHY?
2. You have been offered two stores for sale and can afford only one at this time.  The first is 500 ft2, 6 parking places and in a neighborhood with a household income of 50,000/yr. The other is 560 ft2, 8 parking places in an area with a household income of 42,500/yr.  Which store should have higher daily sales?

Problem 3. A Trucking company has just purchased 30 additional trucks for each of three warehouses (Charlotte, Memphis and Louisville) to ship merchandise to terminals in St Louis, Atlanta and New York. The maximum additional capacity at each terminal is 40, 60 and 50 truckloads per week. Any warehouse can complete 2 trips per week to the St Louis and Atlanta terminals, but only one trip per week to NY.

The average profits/truckload for shipments from warehouses to terminal are given below
Warehouse        St. Louis Atlanta New York
Charlotte           1800     2100     1600
Memphis           1000       700       900
Louisville          1400       800     2200

How many trucks should be assigned to each route to maximize total profit?

St. Louis can absorb an additional 20 truckloads per week at a reduction in unit profit of $300/truckload. Should they plan on this? Why or Why not?

Would it make sense to use another allocation of trucks than giving each warehouse 30 trucks?  If so, what is the most profitable allocation?

Problem 4. A Steak House operates with 2 full time employees who work 8 hours per day plus a number of part-time employees who work 2 or 3 hour shifts during peak meal times. Management wants to develop a schedule for part time employees that will minimize labor costs and still provide customer service. The steak house is open from 11:00am until 10:00pm. Part-time employees are paid $7.60/hr. The total number of  employees needed for each hour is shown in the table below:

One full time employee comes on duty at 11:00 am, works 4 hours, takes a 1 hr break and works another 4 hrs. The second full time employee comes to work at 1pm and works the same 4-1-4 pattern.

Develop a minimum cost schedule (of start-times and 2hr and 3hr shift assignments) for the part-time employees? What is the daily labor expense for part-time employees?