Question

(1) Scott and Associates, Inc. is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows:

client	A	B	C
	(days)	(days)	(days)
Project Leader
Jackson	10	16	32
Ellis	14	22	40
Smith	22	24	34

Each project is assigned to a different leader. How should the projects be assigned to minimize the total number of days spent on the projects?

Hint     -           define a variable for each leader-client pair which is

                                    =          1                      if the leader is assigned to that project

                                    =          0                      if the leader is not assigned to that project

(This is a special case of the TRANSPORTATION PROBLEM (called the Assignment Problem) with SUPPLY and DEMAND are all equal to 1. Do not put into SOLVER that the variables are binary; it always happens.            (There are 6 constraints in total)

1. Formulate a linear programming model for this problem
2. Solve the model using SOLVER
3. Suppose there was an additional project leader, Burton, who has the following times, 14, 18, 36.   Should Burton be used? What is the new total time?
4. If the goal is to minimize the time the whole set of projects is completed, who should be assigned which projects?

(2) Sailco Corporation must determine how many sailboats to produce during each of the next four quarters. The demand during each of the next four quarters is in the table below.

	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Demand	40	60	75	25

At the beginning of the first quarter, Sailco has an inventory of 10 sailboats. At the beginning of each quarter, Sailco must decide how many sailboats to produce during the quarter. For simplicity, we assume that sailboats manufactured in that quarter can be used to meet demand for that quarter. During each quarter, Sailco can produce up to 40 sailboats with regular-time labor at a total cost of $400 per sailboat. By having employees work overtime during a quarter, Sailco can produce additional sailboats with overtime labor at $450 per sailboat. At the end of each quarter (after production has occurred and the current quarter’s demand has been satisfied), a holding cost of $20 per sailboat is incurred. Determine a production schedule to minimize the sum of production and inventory holding costs during the next four quarters

1. Formulate a linear programming model for this problem       (A Spreadsheet approach is easier.)
2. Solve the model using SOLVER.
3. Suppose the holding cost is not $20 but some other number. For what levels of holding cost per quarter is the optimal solution in “b” still optimal?

Answer 1