What is the least expensive redistribution plan for the vehicles? Which location still hasexcess vehicle(s) and how many?

To determine the least expensive redistribution plan for vehicles, we need to analyze the current vehicle distribution across various locations, the demand for vehicles at each location, and any transportation costs associated with moving vehicles from one area to another.

Step 1: Break Down the Problem

1. Identify the starting number of vehicles at each location and the demand at each location.
2. Calculate the excess or deficit of vehicles at each location.
3. Assess the transportation costs associated with moving vehicles between locations.

Step 2: Relevant Concepts

1. Excess and Shortage Calculation:

   • For each location, compute excess vehicles as: $\text{Excess}_i = \text{Vehicles}_i - \text{Demand}_i$
   • A positive value indicates excess vehicles, while a negative indicates a shortage.

2. Cost Minimization:

   • Determine the transportation costs based on the distance and number of vehicles to transport.

Step 3: Analysis and Detail

1. Identify Each Location:

   • Let’s assume three locations A, B, and C with vehicles and demands denoted as: $\text{Vehicles}_A, \text{Demand}_A, \text{Vehicles}_B, \text{Demand}_B, \text{Vehicles}_C, \text{Demand}_C$

2. Calculate Excess Vehicles:

   • Calculate for each location. For example, if:
     • $\text{Vehicles}_A = 10, \text{Demand}_A = 8$
     • $\text{Vehicles}_B = 5, \text{Demand}_B = 7$
     • $\text{Vehicles}_C = 4, \text{Demand}_C = 6$

   Then:

   • $\text{Excess}_A = 10 - 8 = 2 \quad (\text{Excess at A})$
   • $\text{Excess}_B = 5 - 7 = -2 \quad (\text{Shortage at B})$
   • $\text{Excess}_C = 4 - 6 = -2 \quad (\text{Shortage at C})$

3. Redistribution Plan:

   • Move vehicles from A to B and C based on excess and shortage.
   • Calculate the total cost of transportation for the planned vehicle transfers.

Step 4: Verify and Summarize

Check the calculations:

• Ensure the total number of vehicles redeployed meets the demands without exceeding available excess.
• Review transportation costs.

Final Answer

The least expensive redistribution plan is to move 2 vehicles from location A, which has 2 excess vehicles, to location B (2 vehicles needed) and potentially another 2 to C if further analysis shows costs are acceptable. Therefore, the final distribution should zero out any excess at A, leaving the final vehicle counts balanced or within acceptable limits of demand.

In summary, location A will have zero excess vehicles, while locations B and C will still have shortages. Details would vary based on actual distances and vehicle transformation costs, which need to be included in the complete analysis for optimized cost effectiveness.