Discuss the below:
Q1: The personnel manager for a large corporation feels that there may be a relationship between absenteeism and the age of workers. The manager would like to use the age of a worker to develop a model to predict the number of days absent during a calendar year. A random sample of 5 workers was selected with the results presented below:
|
Worker
|
Age in years (X)
|
Days absent (Y)
|
(Xi- X‾)2
|
(Yi- Y‾)2
|
(Xi- X‾)(Yi- Y‾)
|
|
1
|
27
|
15
|
|
|
|
|
2
|
61
|
6
|
|
|
|
|
3
|
37
|
10
|
|
|
|
|
4
|
23
|
18
|
|
|
|
|
5
|
46
|
9
|
|
|
|
|
|
=
X‾
|
=
Y‾
|
SSXX =
|
SSYY =
|
SS XY =
|
a) Compute, , SSXX , SSYY , SS XY in the table above. And work the problem on excel also, showing step by step.
b) Determine the sample correlation coefficient between age and number of days absent.
c) Determine the regression equation using number of days absent as the dependent variable.
d) Compute the standard error of the estimate se.
Q2: The Italian General's Pizza Parlour is a small restaurant catering to patrons with a taste for European pizza. One of its specialties is Italian Prize pizza. The manager must forecast weekly demand for these special pizzas so that he can order pizza shells weekly. Recently, the demand has been as follows:
|
Week
|
Number of Pizzas Sold
|
|
June 2-8
|
48
|
|
June 9-15
|
62
|
|
June 16-22
|
49
|
|
June 23-29
|
55
|
|
June 30-July 6
|
51
|
|
July 7-13
|
59
|
a) Forecast the demand for pizzas for all weeks from June 23 to July 20. Use a three-month weighted moving average with weights of 0.2, 0.3, and 0.5. Note: Show all calculations here and work the problem on excel also, showing step by step. Use the largest weight with the most recent data.
|
Week
|
Number of Pizzas Sold
|
Forecast
|
|
June 2-8
|
48
|
|
|
June 9-15
|
62
|
|
|
June 16-22
|
49
|
|
|
June 23-29
|
55
|
|
|
June 30-July 6
|
51
|
|
|
July 7-13
|
59
|
|
|
July 14-20
|
|
|
b) Forecast the demand using exponential smoothing with alpha = 0.2 for all weeks from June 16 to July 20. Use the sales for the week June 2-8 as the starting forecast for the week June 9-15 as given. Note: Show all calculations here and work the problem on excel also, showing step by step..
|
Week
|
Number of Pizzas Sold
|
Forecast
|
|
June 2-8
|
48
|
|
|
June 9-15
|
62
|
48
|
|
June 16-22
|
49
|
|
|
June 23-29
|
55
|
|
|
June 30-July 6
|
51
|
|
|
July 7-13
|
59
|
|
|
July 14-20
|
|
|
c) Which of the methods in parts (a) and (b) produces better forecasts for the weeks 4-6? Answer on the basis of a measure of mean absolute deviation (MAD).
|
Week
|
Number of Pizzas Sold
|
|
|
|
|
|
June 23-29
|
55
|
|
|
|
|
|
June 30-July 6
|
51
|
|
|
|
|
|
July 7-13
|
59
|
|
|
|
|
|
|
|
|
|
|
|
Q3: Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen. Pay-off table for the problem is given below. Apply each of the criteria given below to determine the decision Weiss should make.
|
|
Demand for Red Roses
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
0
|
0
|
0
|
|
Order 25 dozen
|
625
|
625
|
625
|
|
Order 60 dozen
|
100
|
1500
|
1500
|
|
Order 130 dozen
|
-950
|
450
|
3250
|
a) Optimistic or Maximax Criterion
|
|
Demand for Red Roses
|
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
0
|
0
|
0
|
|
|
Order 25 dozen
|
625
|
625
|
625
|
|
|
Order 60 dozen
|
100
|
1500
|
1500
|
|
|
Order 130 dozen
|
-950
|
450
|
3250
|
|
Decision:
b)Pessimistic or Maximin Criterion
|
|
Demand for Red Roses
|
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
0
|
0
|
0
|
|
|
Order 25 dozen
|
625
|
625
|
625
|
|
|
Order 60 dozen
|
100
|
1500
|
1500
|
|
|
Order 130 dozen
|
-950
|
450
|
3250
|
|
Equally likely or Principle of Insufficient Reason Criterion
|
|
Demand for Red Roses
|
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
0
|
0
|
0
|
|
|
Order 25 dozen
|
625
|
625
|
625
|
|
|
Order 60 dozen
|
100
|
1500
|
1500
|
|
|
Order 130 dozen
|
-950
|
450
|
3250
|
|
c) Criterion of realism with coefficient of realism = 0.6
|
|
Demand for Red Roses
|
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
0
|
0
|
0
|
|
|
Order 25 dozen
|
625
|
625
|
625
|
|
|
Order 60 dozen
|
100
|
1500
|
1500
|
|
|
Order 130 dozen
|
-950
|
450
|
3250
|
|
d) Minimax Regret Approach
|
|
Demand for Red Roses
|
|
|
Alternative
|
Low (25 dozen)
|
Medium (60 dozen)
|
High (130 dozen)
|
|
Do nothing
|
|
|
|
|
|
Order 25 dozen
|
|
|
|
|
|
Order 60 dozen
|
|
|
|
|
|
Order 130 dozen
|
|
|
|
|
Q4: The Exeter Company produces two basic types of dog toys. Two resources are crucial to the output of the toys: assembling hours and packaging hours. Further, only a limited quantity of type 1 toy can be sold. The linear programming model given below was formulated to represent next week's situation.
Let, X1 = Amount of type A dog toy to be produced next week
X2 = Amount of type B dog toy to be produced next week
Maximize total contribution Z = 35 X1 + 40 X2
Subject to
Extrusion hours: 4 X1 + 6 X2 £ 48
Packaging hours: 2 X1 + 2 X2 £ 18
Sales Potential: X1 < 6
Non-negativity: X1 ³ 0, X2 ³ 0
Use Excel Solver different work sheets per problem
Note 1: Place X1 along the horizontal axis and X2 along the vertical axi.
Note 2: Clearly mark the feasible region on the graph.
Note 3: Find the points of intersection points algebraically.
Note 4: Clearly show all steps to find the optimal solution by the graphical method.
X2