1. The problem involves analyzing origin-destination (O-D) data and travel time matrices for 6 zones in a transportation planning context. 2. Given: - O-D matrix with outflows $O_i$ and inflows $D_d$ for each zone. - Travel time matrix between zones. - Parameter $\alpha = 0.4XX2$ (likely a typo, assuming $\alpha = 0.4 \times 2 = 0.8$ for calculation). 3. Objective: Typically, such problems require calculating trip distribution using a gravity model: $$T_{ij} = k \times O_i \times D_j \times e^{-\alpha t_{ij}}$$ where $T_{ij}$ is trips from zone $i$ to $j$, $t_{ij}$ is travel time, and $k$ is a balancing factor. 4. Steps: - Use the given $O_i$ and $D_j$ values from Table 1. - Use travel times $t_{ij}$ from Table 2. - Calculate $e^{-\alpha t_{ij}}$ for each pair. - Compute preliminary $T_{ij}$ values. - Adjust $k$ to satisfy constraints (e.g., sum of trips from $i$ equals $O_i$). 5. Example calculation for $T_{1,2}$: - $O_1 = 280$, $D_2 = 320$, $t_{1,2} = 14$ - $\alpha = 0.8$ - Calculate $e^{-0.8 \times 14} = e^{-11.2} \approx 1.36 \times 10^{-5}$ - Preliminary $T_{1,2} = k \times 280 \times 320 \times 1.36 \times 10^{-5} = k \times 1.22$ 6. Repeat for all $i,j$ pairs to form matrix $T$. 7. Determine $k$ by ensuring row sums equal $O_i$. 8. This process models trip distribution based on travel time and trip productions/attractions. Final answer: The gravity model formula and method to compute trip distribution matrix $T_{ij}$ using given data and parameter $\alpha$.