Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Part 1

The director of the Riley​ County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4​ weeks:

                                                                                            

 

Mon

Tue

Wed

Thu

Fri

Sat

Week 1

210

178

250

215

160

180

Week 2

215

180

250

213

165

185

Week 3

220

176

260

220

175

190

Week 4

225

178

260

225

176

190

Part 2

​a) Calculate a seasonal index for each day of the week ​(enter your responses rounded to three decimal​ places).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Part 3

​b) Let x

 

=1 for Monday of Week 1. If the trend equation for this problem​ is:

 

 

 

y

 

=201.74

 

+​0.18x,

 

the forecast for each day of week 5 is ​(round your responses to the nearest whole​ number):

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

### Forecasting Evening Patron Usage at Riley County, Kansas Library

The Director of the Riley County, Kansas library system is looking to forecast evening patron usage for the upcoming week. Below are the data for the past 4 weeks:

|    | Mon | Tue | Wed | Thu | Fri | Sat |
|----|-----|-----|-----|-----|-----|-----|
| **Week 1** | 210 | 178 | 250 | 215 | 160 | 180 |
| **Week 2** | 215 | 180 | 250 | 213 | 165 | 185 |
| **Week 3** | 220 | 176 | 260 | 220 | 175 | 190 |
| **Week 4** | 225 | 178 | 260 | 225 | 176 | 190 |

**a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places).**

| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Seasonal index**  |     |     |     |     |     |     |

**b) Let \( x = 1 \) for Monday of Week 1. If the trend equation for this problem is:**

\[ \hat{y} = 201.74 + 0.18x \]

The forecast for each day of Week 5 is (round your responses to the nearest whole number):

| **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat |
|---------------------|-----|-----|-----|-----|-----|-----|
| **Forecast**        |     |     |     |     |     |     |

### Explanatory Notes:

- **Seasonal Index Calculation**:
  - A seasonal index is a value that represents how a certain time period's data values compare to the typical or average data values.
  - Typically, a seasonal index is calculated by finding the average value for each day, then dividing each day’s average by the overall average for all days.

- **Trend Equation**:
  - The trend equation provided \( \hat{y} = 201.74 + 0.18x \) calculates a predictive value \( \hat{y} \) based on the value of x.
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Transcribed Image Text:### Forecasting Evening Patron Usage at Riley County, Kansas Library The Director of the Riley County, Kansas library system is looking to forecast evening patron usage for the upcoming week. Below are the data for the past 4 weeks: | | Mon | Tue | Wed | Thu | Fri | Sat | |----|-----|-----|-----|-----|-----|-----| | **Week 1** | 210 | 178 | 250 | 215 | 160 | 180 | | **Week 2** | 215 | 180 | 250 | 213 | 165 | 185 | | **Week 3** | 220 | 176 | 260 | 220 | 175 | 190 | | **Week 4** | 225 | 178 | 260 | 225 | 176 | 190 | **a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places).** | **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat | |---------------------|-----|-----|-----|-----|-----|-----| | **Seasonal index** | | | | | | | **b) Let \( x = 1 \) for Monday of Week 1. If the trend equation for this problem is:** \[ \hat{y} = 201.74 + 0.18x \] The forecast for each day of Week 5 is (round your responses to the nearest whole number): | **Day of the week** | Mon | Tue | Wed | Thu | Fri | Sat | |---------------------|-----|-----|-----|-----|-----|-----| | **Forecast** | | | | | | | ### Explanatory Notes: - **Seasonal Index Calculation**: - A seasonal index is a value that represents how a certain time period's data values compare to the typical or average data values. - Typically, a seasonal index is calculated by finding the average value for each day, then dividing each day’s average by the overall average for all days. - **Trend Equation**: - The trend equation provided \( \hat{y} = 201.74 + 0.18x \) calculates a predictive value \( \hat{y} \) based on the value of x.
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