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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?

Respuesta :

Answer:

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]

a. When Two Locations have same Total Cost at output is 120

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

Calculation of Fixed Cost

When the Total Fixed Cost is = Total Fixed Cost + Total Variable Cost

Then Location A :

After that The Total Cost A is = 800000 + 14000x

Now, Location B : The Total Cost of B is = 920000 + 13000x

a. When Two Locations have same Total Cost at output is:

Then TC (A) is = TC (B)

After that 800000 + 14000x = 920000 + 13000x

Now, 920000 - 800000 = 14000x - 13000x

Then 120000 = 1000x

Therefore, x = 120000 / 1000 → = 120

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

Hit & Trial method ; taking x is = 100

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

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

After that Hit & Trial method ; taking x = 150

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

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