14. A vehicle oil change company is seeking a new site for its service center. The fixed cost and variable cost per vehicle 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: B
Site 3 is the optimal location for the new service center.
To determine the best site for the new service center, we need to calculate the total cost for servicing 800 vehicles at each location and compare them. Site 3 has the lowest total cost when considering both fixed and variable costs.
A) Site 1
Site 1 has a fixed cost of $6500 and a variable cost of $3 per vehicle. The total cost for servicing 800 vehicles would be $6500 + ($3 * 800) = $6500 + $2400 = $8900. While this is a viable option, it is not the most cost-effective compared to Site 3.
B) Site 3
Site 3 has a fixed cost of $4000 and a variable cost of $4 per vehicle. The total cost for servicing 800 vehicles would be $4000 + ($4 * 800) = $4000 + $3200 = $7200. This total cost is the lowest among all the sites, making it the best choice for the new service center.
C) Site 2
Site 2 has a fixed cost of $3500 and a variable cost of $5 per vehicle. The total cost for servicing 800 vehicles would be $3500 + ($5 * 800) = $3500 + $4000 = $7500. Although this option is less expensive than Site 1 and Site 4, it is still higher than the total cost at Site 3.
D) Site 4
Site 4 has a fixed cost of $5000 and a variable cost of $6 per vehicle. The total cost for servicing 800 vehicles would be $5000 + ($6 * 800) = $5000 + $4800 = $9800. This is the highest total cost among all options, making it the least desirable choice for the service center.
Conclusion
Site 3 is the optimal location due to its total cost of $7200, which is lower than the costs associated with Site 1, Site 2, and Site 4. All other sites have higher total costs, making them less favorable options for the new service center.