A small producer of machine tools wants to move to a larger building and has identified two alternatives. Location A has annual fixed costs of $800,000 and variable costs of $14,000 per unit; location B has annual fixed costs of $920,000 and variable costs of $13,000 per unit. The finished items sell for $17,000 each.
a. At what volume of output would the two locations have the same total cost?
b. For what range of output would location A be superior? For what range would B be superior?

Locations Same Total Cost at output = 120

Location A superior (less TC) than Location B (more TC) at output = 100

Location B superior (less TC) than Location A (more TC) at output = 150

Explanation:

Total Fixed Cost = Total Fixed Cost + Total Variable Cost

Location A :

Total Cost A  = 800000 + 14000x

Location B :

Total Cost B = 920000 + 13000x

a. Two Locations have same Total Cost at output :

TC (A) = TC (B)

800000 + 14000x = 920000 + 13000x

920000 - 800000 = 14000x - 13000x

120000 = 1000x

x = 120000 / 1000 → = 120

b. Location A would be superior if : TC (A) < TC (B)

Hit & Trial method ; taking x = 100

[800000 + 14000 (100) = 220000] < [920000 + 13000 (100) = 2220000]

Location B would be superior if : TC (B) < TC (A)

Hit & Trial method ; taking x = 150

800000 + 14000 (150) = 2900000] > [920000 + 13000 (150) = 2870000]

explanation: doctrine of respondeat superior is a legal doctrine that is commonly used in tort. this principle makes an employer or principal legally responsible for the wrongful acts done by an employee or agent, if such acts occur within the scope of the employment or agency.