1. The quarterly sales data (number of copies sold) for a college textbook over the past 3 years are as follows in the Table below:
QUARTERLY SALES
Quarter Year 1 Year 2 Year 3
1 16 18 18
2 9 9 11
3 26 29 29
4 25 23 26
a) Compute seasonal indexes for the 4 quarters.
b) When does the textbook publisher experience the largest change in sales? Does this result appear to be reasonable? Explain.
c) Using the information on seasonality, compare a 4-quarter moving average to trend projection model and an exponential smoothing with a smoothing constant of 0.2.
d) Use the selected model to generate a forecast for sales for the first quarter of Year 4.
2. Office Automation Inc., has developed a proposal for introducing a new computerized office system that will improve word processing and interoffice communications for a particular company. Contained in the proposal is a list of activities that must be accomplished in order to complete the new office system project. Information about the activities is shown in the table below. Times are in weeks.
Data for Office Automation, Inc.
Activity Description Immediate Predecessors Normal Time
A Plan needs ———– 10
B Order equipment A 8
C Install equipment B 10
D Set up training lab A 7
E Training course D 10
F Testing system C, E 3
a). Show the network for the project.
b). Develop an activity schedule for the project using normal times.
c). What are the critical path activities and what is the expected project completion time?
3. Consider the following transportation problem. XYZ Company has capacities of 600 in its Corning plant and 200 in it plant in Geneva. However, its demands come from Fairport, Mendon, and Penfield at the following demand levels 300, 200, and 300 respectively.
The transportation costs per unit are as follows:
Fairport Mendon Penfield
Corning 16 10 14
Geneva 12 12 20
a) Develop a linear programming formulation of this transportation problem.
b) Use Excel Solver to solve this problem and find the optimal solution.
4. Consider the following linear program
Max 3×1 + 2×2
s.t.
1×1 + 1×2 < 10
3×1 + 1×2 < 24
1×1 + 2×2< 16
And x1, x2 > 0.
a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of x1, x2, and Z.
b) Assume that the objective function coefficient for x1 changes from 3 to 5. Does the optimal solution change?
c) Assume that the objective function coefficient for x1 remains 3, but the objective function coefficient for x2 changes from 2 to 4. Does the optimal solution change?
d) What are the shadow prices for these constraints?
e) What conclusions can you draw about changes to the right hand side of constraint 2?
f) Identify the binding and non-binding constraints in this problem and explain.
