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?
Site 3 offers the lowest total cost for servicing 800 vehicles.
To determine the best location for the service center, we need to calculate the total cost for each site based on the fixed and variable costs associated with servicing 800 vehicles. Site 3, with a fixed cost of $4000 and a variable cost of $4 per vehicle, results in the lowest total cost.
Site 1 has a fixed cost of $6500 and a variable cost of $3 per vehicle. For 800 vehicles, the total cost would be $6500 + ($3 * 800) = $6500 + $2400 = $8900. This is higher than the total cost at Site 3.
Site 3 features a fixed cost of $4000 and a variable cost of $4 per vehicle. The total cost for servicing 800 vehicles at this site is $4000 + ($4 * 800) = $4000 + $3200 = $7200. This total is the lowest among all sites, making it the most cost-effective option.
Site 2 has a fixed cost of $3500 and a variable cost of $5 per vehicle. The total cost in this case would be $3500 + ($5 * 800) = $3500 + $4000 = $7500. While this is lower than Site 1 and Site 4, it is still higher than the cost at Site 3.
Site 4 has a fixed cost of $5000 and a variable cost of $6 per vehicle. For 800 vehicles, the total cost comes to $5000 + ($6 * 800) = $5000 + $4800 = $9800. This is the highest total cost among all the sites.
After analyzing the total costs for each potential site, Site 3 emerges as the best choice due to its lowest total cost of $7200 for servicing 800 vehicles. This highlights the importance of considering both fixed and variable costs when making financial decisions about service center locations.
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