FreshBrew, a company that produces premium coffee machines, is planning to open a new manufacturing facility. Management has narrowed the search to three potential communities. The expected demand for coffee machines is 10,000 units per year. They estimate the fixed costs per year and variable costs per unit for each location as follows:

Community

Fixed Costs ($/year)

Variable Costs ($/unit)

A

100,000

20

B

120,000

15

C

150,000

10

Based on the Break-Even Analysis, which community should FreshBrew choose for the new facility at what total annual cost?

Question

FreshBrew, a company that produces premium coffee machines, is planning to open a new manufacturing facility. Management has narrowed the search to three potential communities. The expected demand for coffee machines is 10,000 units per year. They estimate the fixed costs per year and variable costs per unit for each location as follows:

Community

Fixed Costs ($/year)

Variable Costs ($/unit)

A

100,000

20

B

120,000

15

C

150,000

10

Based on the Break-Even Analysis, which community should FreshBrew choose for the new facility at what total annual cost?

BlackTom AI · Accepted Answer

FreshBrew is evaluating three communities for a new manufacturing facility. The key numbers are:
- Demand (annual output): 10,000 units
- For each community, total annual cost = fixed costs per year + (variable cost per unit × annual quantity)

Option A: Fixed = 100,000; Variable = 20 per unit
- Total annual cost = 100,000 + (20 × 10,000) = 100,000 + 200,000 = 300,000
- This yields a total cost of 300k, which is higher than the other locations based on the given demand.

Option B: Fixed = 120,000; Variable = 15 per unit
- Total annual cost = 120,000 + (15 × 10,000) = 120,000 + 150,000 = 270,000
- This results in a total cost of 270k, lower than A but still above C.

Option C: Fixed = 150,000; Variable = 10 per unit
- Total annual cost = 150,000 + (10 × 10,000) = 150,000 + 100,000 = 250,000
- This gives the lowest total cost among the three options at 250k.

Now compare the options directly:
- A costs 300,000
- B costs 270,000
- C costs 250,000
Thus, the cost-minimizing choice under the given annual quantity is Community C, since it yields the smallest total annual cost.

Consider a potential pitfall: if one trusts only fixed costs, it might mislead toward the lowest fixed cost, but in break-even or cost-minimization analyses like this, the total cost function matters most for the specified quantity; here, the per-unit savings at C (10 vs 20 or 15) more than compensate for its higher fixed cost, producing the least total cost at 10,000 units.

If someone wonders about the effect of changing demand: as annual quantity increases or decreases, the difference in variable costs will impact the total cost differently, but with the current 10,000-unit assumption, C remains the lowest-cost option.

Finally, evaluating the provided answer options:
- 'Community C — Total Cost = $250,000' is the statement that aligns with the calculation above.
- 'Based on the Break-Even Analysis, which community should FreshBrew choose for the new facility at what total annual cost?' is a restatement of the problem rather than a computed cost.
- 'Community B — Total Cost = $270,000' presents the cost for B, which is higher than C.
- 'Community B — Total Cost = $230,000' presents an incorrect cost for B, miscomputing either fixed or variable contributions.

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