Question

Two different manufacturing processes are being considered for making a new product. The first process is less​ capital-intensive, with fixed costs of only $ 48,900 per year and variable costs of $ 690 per unit. The second process has fixed costs of $ 408,000 but variable costs of only $ 165 per unit.

What is the​ break-even quantity, beyond which the second process becomes more attractive than the​ first?

The volume at which the second process becomes more attractive is _______ units. ​(Enter your response rounded to the nearest whole​ number.)

Answer 1

The break-even quantity, beyond which the second process becomes more attractive than the first, is approximately 858 units.

Step-by-step explanation:

The break-even quantity occurs when the total costs of the two processes are equal. Let's calculate the break-even quantity.

For the first process, the total cost is given by:

Total Cost = Fixed Costs + (Variable Costs * Quantity)

TC1 = $48,900 + ($690 * Q)

For the second process, the total cost is given by:

Total Cost = Fixed Costs + (Variable Costs * Quantity)

TC2 = $408,000 + ($165 * Q)

Setting TC1 = TC2, we have:

$48,900 + ($690 * Q) = $408,000 + ($165 * Q)

Solving for Q, we find Q = 858.

Therefore, the break-even quantity, beyond which the second process becomes more attractive than the first, is approximately 858 units.