Question

A labor-intensive process to manufacture a product has a fixed cost of $338,000 and a variable cost of $143 per unit. An automated process for the same product has a fixed cost of $1,244,000 and a variable cost of $92.50 per unit. How many units must be produced and sold at $197 each for the automated process to be the preferred over the labor-intensive process?

Answer 1

no of unit is 17941

Step-by-step explanation:

given data

fixed cost = $338,000

variable cost = $143 per unit

fixed cost = $1,244,000

variable cost = $92.50 per unit

solution

we consider here no of unit is = n

so here total cost of labor will be sum of fix and variable cost i.e

total cost of labor = $33800 + $143 n ..........1

and

total cost of capital intensive = $1,244,000 + $92.5 n ..........2

so here in both we prefer cost of capital if cost of capital intensive less than cost of labor

$1,244,000 + $92.5 n < $33800 + $143 n

solve we get

n >
`(906000)/(50.5)`

n > 17941

and

cost of producing less than selling cost so here

$1,244,000 + $92.5 n < 197 n

solve it we get

n >
`(1244000)/(104.5)`

n > 11904

so in both we get greatest no is 17941

so no of unit is 17941