1. Baltimore Manufacturing Co. makes two products, tables and chairs, which must be processed through assembly and finishing departments. Each table requires 6 hours to assemble and 4 hours to finish, but each chair requires 3 hours to assemble and 5 hours to finish. Assembly department has 90 hours available, and finishing department can handle up to 80 hours of work. The company wants to see at least 4 chairs and at least 5 tables produced during the production. The production of table must exceed the production of chair. Each table yields a profit of $8, and each chair can be sold for a profit of $6. Show the feasible region graphically (Draw a graph by using MS WORD's 'Shapes' under the 'Insert' tab).
a. What are the extreme points of the feasible region?
b. Find the optimal solution using the graphical method.
c. Are there any slack values? Are there any surplus values?
d. Compute the shadow prices of each constraint.
2. Scott Armstrong, the managing editor of Your Horoscope magazine, needs to develop a forecasting system for monthly newsstand sales in order to schedule press runs. Sales in thousands of copies for the first 7 months of publication were:
| Year |
Month
|
Sales
|
|
2013
|
April
|
65
|
|
|
May
|
70
|
|
|
June
|
80
|
|
|
July
|
82
|
|
|
August
|
90
|
|
|
September
|
82
|
|
|
October
|
86
|
Scott does not believe there is a seasonal pattern. He is considering three different forecasting models: three-period moving average, simple exponential smoothing with, and time series regression (i.e., trend projection). Determine the best forecasting model among the above three methods, and develop a forecast for November 2013. Use the first four months as the warm-up sample period and the remaining months as the forecasting sample period. The criteria of measuring forecast accuracy to be used are Bias, MAD, MSE, and MAPE. Refer to the PowerPoint lecture notes posted on the course home page.