BMW is trying to decide where to locate a new factory. It is considering three locations in three different states. The goal is to locate in the lowest-cost site, where cost is measured by the annual fixed costs (state taxes) plus the variable costs of production. BMW has gathered the following data regarding its top three options: Site Annual Fixed CostVariable Cost per VehicleA $14,750,000 $26,850B $16,500,000 $25,850C $19,250,000 $25,350What is the break-even volume (units of production) between Site A and Site B? (Display your answer as a whole number.) What is the break-even volume (units of production) between Site B and Site C? (Display your answer as a whole number.)
Question
BMW is trying to decide where to locate a new factory. It is considering three locations in three different states. The goal is to locate in the lowest-cost site, where cost is measured by the annual fixed costs (state taxes) plus the variable costs of production. BMW has gathered the following data regarding its top three options: Site Annual Fixed CostVariable Cost per VehicleA 26,850B 25,850C 25,350What is the break-even volume (units of production) between Site A and Site B? (Display your answer as a whole number.) What is the break-even volume (units of production) between Site B and Site C? (Display your answer as a whole number.)
Solution
To calculate the break-even volume between two sites, we need to set the total cost of production at both sites equal to each other and solve for the volume. The total cost of production is the sum of the fixed costs and the variable costs (which depend on the volume of production).
- Break-even volume between Site A and Site B:
Let X be the volume of production. We have:
14,750,000 + 26,850X = 16,500,000 + 25,850X
Solving this equation for X gives us:
X = (16,500,000 - 14,750,000) / (26,850 - 25,850) = 1,750,000 / 1,000 = 1,750 units
So, the break-even volume between Site A and Site B is 1,750 units.
- Break-even volume between Site B and Site C:
Again, let X be the volume of production. We have:
16,500,000 + 25,850X = 19,250,000 + 25,350X
Solving this equation for X gives us:
X = (19,250,000 - 16,500,000) / (25,850 - 25,350) = 2,750,000 / 500 = 5,500 units
So, the break-even volume between Site B and Site C is 5,500 units.
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