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2. A zone's HBW trip production and attraction tables have been determined as shown below. The total production is not equal to the total attraction. Balance the trip productions and attractions. HBW trips HBW trips Zone i 1 2 3 Total P₁ 300 100 200 600 Zone j 1 2 3 Total Aj 150 300 350 800

2. A zone's HBW trip production and attraction tables have been determined as shown below. The total production is not equal to the total attraction. Balance the trip productions and attractions. HBW trips HBW trips Zone i 1 2 3 Total P₁ 300 100 200 600 Zone j 1 2 3 Total Aj 150 300 350 800

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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HBW stands for Home based work

### Balancing HBW Trip Production and Attraction Tables A zone's Home-Based Work (HBW) trip production and attraction tables have been determined as shown below. The total production is not equal to the total attraction. The objective is to balance the trip productions and attractions accordingly. #### HBW Trip Production Table | Zone \(i\) | \(P_i\) | |------------|---------| | 1 | 300 | | 2 | 100 | | 3 | 200 | | **Total** | **600** | #### HBW Trip Attraction Table | Zone \(j\) | \(A_j\) | |------------|---------| | 1 | 150 | | 2 | 300 | | 3 | 350 | | **Total** | **800** | The production table (left) shows the total number of trips produced in each zone \(i\), while the attraction table (right) shows the total number of trips attracted to each zone \(j\). ### Explanation - **Zone \(i\)** and **Zone \(j\)** represent different zones. - **\(P_i\)** refers to the number of trips produced in zone \(i\). - **\(A_j\)** refers to the number of trips attracted to zone \(j\). - The total production (\(600\) trips) is less than the total attraction (\(800\) trips). #### Balancing the Tables To balance the tables, the following must be achieved: 1. **Adjustment of Productions or Attractions:** - The total amount of trips produced should match the total amount of trips attracted. ##### Methods to Balance 1. **Scale Productions to Match Attractions:** - Adjust the production values proportionally to match the attraction totals. For example, increasing each production value so that their sum matches 800. 2. **Scale Attractions to Match Productions:** - Adjust the attraction values proportionally to match the production total. For example, decreasing each attraction value so that their sum matches 600. Either method involves applying scaling factors to adjust the values, ensuring the new totals for production and attraction are equal, thus achieving balance.
Transcribed Image Text:### Balancing HBW Trip Production and Attraction Tables A zone's Home-Based Work (HBW) trip production and attraction tables have been determined as shown below. The total production is not equal to the total attraction. The objective is to balance the trip productions and attractions accordingly. #### HBW Trip Production Table | Zone \(i\) | \(P_i\) | |------------|---------| | 1 | 300 | | 2 | 100 | | 3 | 200 | | **Total** | **600** | #### HBW Trip Attraction Table | Zone \(j\) | \(A_j\) | |------------|---------| | 1 | 150 | | 2 | 300 | | 3 | 350 | | **Total** | **800** | The production table (left) shows the total number of trips produced in each zone \(i\), while the attraction table (right) shows the total number of trips attracted to each zone \(j\). ### Explanation - **Zone \(i\)** and **Zone \(j\)** represent different zones. - **\(P_i\)** refers to the number of trips produced in zone \(i\). - **\(A_j\)** refers to the number of trips attracted to zone \(j\). - The total production (\(600\) trips) is less than the total attraction (\(800\) trips). #### Balancing the Tables To balance the tables, the following must be achieved: 1. **Adjustment of Productions or Attractions:** - The total amount of trips produced should match the total amount of trips attracted. ##### Methods to Balance 1. **Scale Productions to Match Attractions:** - Adjust the production values proportionally to match the attraction totals. For example, increasing each production value so that their sum matches 800. 2. **Scale Attractions to Match Productions:** - Adjust the attraction values proportionally to match the production total. For example, decreasing each attraction value so that their sum matches 600. Either method involves applying scaling factors to adjust the values, ensuring the new totals for production and attraction are equal, thus achieving balance.
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