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27 March, 04:56

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

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  1. 27 March, 05:22
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    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.

    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.
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