. Location A would result in annual fixed costs of $300,000 and variable costs of $55 per unit. Annual fixed costs at Location B are $600,000 with variable costs of $32 per unit. Sales volume is estimated to be 30,000 units per year. At what volume are the two facilities equal in cost?

Cost Equation calculate the total cost of the products produced / sold in a period. It adds the variable cost of the given numbers of units and Fixed cost for the period to calculate the total cost.

The Total Cost Can be Calculated using following Equation.

y = mx + b

y = Total cost

m = variable cost

b = fixed cost

x = quantity of unit produced / sold

Placing Values in the cost equation at each location.

Location A

y = $55x + $300,000

Location B

y = $32x + $600,000

According to given condition

Cost of Location A = Cost of Location B

$55x + $300,000 = $32x + $600,000

$55x - $32x = $600,000 - $300,000

$23x = $300,000

x= $300,000 / $23 = 13,043.48 units

Check

y = $55 x 13,043.48 + $300,000 = $717,391.4 + $300,000 = $1,017,391.4

Location B

y = $32x 13,043.48 + $600,000 = $417,391.4 + $600,000 = $1,017,391.4

Tundexi Tundexi · Answer 2 · 2022-01-04T11:08:05+01:00

The volume at which the two facilities equal in cost is 13,043.48 units.

The total cost can be calculated using following equation:. y = mx + b where y = Total cost, m = variable cost, b = fixed cost, x = quantity of unit produced / sold.

Placing of values in the cost equation at each location.

Location A

y = $55x + $300,000

Location B

y = $32x + $600,000

According to given condition:

Cost of Location A = Cost of Location B

$55x + $300,000 = $32x + $600,000

$55x - $32x = $600,000 - $300,000

$23x = $300,000

x = $300,000 / $23

x = 13,043.48 units

In conclusion, the volume at which the two facilities equal in cost is 13,043.48 units.