Question

A company is considering two options for the production of a part needed downstream in the manufacturing process. Details about fixed and variable costs are as follows.

Specialized​ automation: Fixed cost= ​$1,395,200 per​ month, Variable cost = ​$13 per unit.
General​ automation: Fixed cost= ​$180,000 per​ month, Variable cost= ​$27 per unit.

What is the monthly​ break-even quantity between the two automation​ approaches?

Answer 1

86,800 units

Step-by-step explanation:

Let 'n' be the number of units produced per month.

The cost function for the Specialized automation option is:

`S = 1,395,200 +13n`

The cost function for the General automation option is:

`G = 180,000 +27n`

Break-even between both options occurs at the production level for which costs are equal:

`S =G\\1,395,200 +13n = 180,000+27n\\n=(1,395,200-180,000)/(14)\\n=86,800\ units`

The monthly​ break-even quantity between the two automation​ approaches is 86,800 units.