Question

A labor-intensive process has a fixed cost of $320,000 and a variable cost of $143 per unit. A capital-intensive (automated) process for the same product has a fixed cost of $1,330,000 and a variable cost of $92.50 per unit. Contributed by Paul R. McCright, University of South Florida. How many units must be produced and sold at $208 each for the automated process to be preferred to the labor-intensive process

Answer 1

More than 20,000 units must be produced and sold at $208 each for the automated process to be preferred to the labor-intensive process.

Step-by-step explanation:

Call X is the number of units must be produced and sold at $208.

For capital-intensive (automated) process, Profit (P) = Sales - fixed cost - variable cost = $208X - $1,330,000 - $92.50x = $115.5x - $1,330,000

For labor-intensive process, Profit (P) = Sales - fixed cost - variable cost = $208X - $320,000 - $143X = $65X - $320,000

The automated process to be preferred to the labor-intensive process when Profit from capital-intensive (automated) process > Profit from labor-intensive process

$115.5x - $1,330,000 > $65X - $320,000

$50.5X > $1,010,000

X > 20,000 (units)

More than 20,000 units must be produced and sold at $208 each for the automated process to be preferred to the labor-intensive process.