Question
In: Operations Management
1. The demand data for a product over the past 5 months are shown below: MONTH...
1. The demand data for a product over the past 5 months are shown below:
|
MONTH |
DEMAND (number of units sold) |
|
Five months ago |
51 |
|
Four months ago |
58 |
|
Three months ago |
63 |
|
Two months ago |
71 |
|
Last month |
77 |
a. Plot the monthly demand data using a software OR on a sheet of graph paper.
b. Use TREND PROJECTIONS method to determine the equation of the trend line estimating the linear relationship between time (in months) and demand (in units sold).
c. Use the equation of the trend line to predict demand for THIS MONTH.
Solutions
Expert Solution
a.
|
# month |
MONTH |
DEMAND |
|
(number of units sold) |
||
|
1 |
Five months ago |
51 |
|
2 |
Four months ago |
58 |
|
3 |
Three months ago |
63 |
|
4 |
Two months ago |
71 |
|
5 |
Last month |
77 |
(b)
|
Slope: |
?=(n?(xy)??x?y)/(n?x2?(?x)2) |
||
|
Offset: |
?=(?y???x)/n |
||
|
Linear regression equation : |
y=?x+? |
||
|
# month (x) |
DEMAND (y) |
xy |
x^2 |
|
1 |
51 |
51 |
1 |
|
2 |
58 |
116 |
4 |
|
3 |
63 |
189 |
9 |
|
4 |
71 |
284 |
16 |
|
5 |
77 |
385 |
25 |
|
Total: |
|||
|
15 |
320 |
1025 |
55 |
|
Slope: |
?= |
6.5 |
|
|
Offset: |
?= |
44.5 |
|
|
Linear Trend Line: |
|||
|
Demand = 6.5(#month)+44.5 |
|||
formulae used:
|
c. Use the equation of the trend line to predict demand for THIS MONTH. |
||
|
# month = |
6 |
|
|
Linear Trend Line: |
Demand = 6.5(#month)+44.5 |
|
|
Demand = 6.5*6+44.5 |
||
|
demand= |
83.5 |
units |
keosha answered 3 months agoRelated Solutions
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