3. A vehicle oil change company is seeking a new site for its service center. The fixed cost and variable cost per vehicle serviced has been estimated as follows: Site 1: Fixed cost of $6500 per month and variable cost of $3 per vehicle; Site 2: Fixed cost of $3500 per month and variable cost of $5 per vehicle; Site 3: Fixed cost of $4000 per month and variable cost of $4 per vehicle; Site 4: Fixed cost of $5000 per month and variable cost of $6 per vehicle. If the number of vehicles estimated to be serviced is 800 per month, and the average service charge per vehicle is $50, where should the new service center be located?
Answer: C
The new service center should be located at Site 3.
Calculating the total cost for servicing 800 vehicles at each site reveals that Site 3 has the lowest total cost, making it the most economical choice for the new service center.
A) Site 4
Site 4 has a fixed cost of $5000 per month and a variable cost of $6 per vehicle. For 800 vehicles, the total cost would be $5000 + ($6 * 800) = $5000 + $4800 = $9800. This total is higher than the cost at Site 3.
B) Site 2
Site 2 has a fixed cost of $3500 per month and a variable cost of $5 per vehicle. The total cost for 800 vehicles would be $3500 + ($5 * 800) = $3500 + $4000 = $7500. While this is lower than Site 4, it is still higher than Site 3's total cost.
C) Site 3
Site 3 has a fixed cost of $4000 per month and a variable cost of $4 per vehicle. The total cost for servicing 800 vehicles would be $4000 + ($4 * 800) = $4000 + $3200 = $7200. This is the lowest total cost among all options, making Site 3 the most favorable choice for the new service center.
D) Site 1
Site 1 has a fixed cost of $6500 per month and a variable cost of $3 per vehicle. The total cost for 800 vehicles would be $6500 + ($3 * 800) = $6500 + $2400 = $8900. This total is significantly higher than the cost at Site 3.
Conclusion
Site 3 is the best option for the new service center as it has the lowest total servicing cost of $7200 compared to the other sites. All other options either have higher fixed or variable costs, making them less economical for servicing 800 vehicles. Therefore, selecting Site 3 aligns with the goal of minimizing operational costs.