A small producer of music boxes wants to move to a larger facility. Two alternat

Question

A small producer of music boxes wants to move to a larger facility. Two alternative facilities have been found. Site 1 has a fixed cost of $500,000 per year, with a variable cost of $25 per unit. Site 2 has a fixed cost of $800,000 per year, but a variable cost of $22 per unit. Write out the equation for total cost for each site. At what volume of output would the two locations have the same total cost? For what range of output would Site 1 be superior? For what range of output would Site 2 be superior? Show your work.

Explanation / Answer

a) Let the no of units produced be: x

Total cost for 1st facility= fixed cost + variable cost

= 500000 + 25*x

Similarly

Total cost for 2nd facility = 800000 + 22*x

b) Total cost for both location is equal

Therefore,

Total cost for 1st facility = total cost for 2nd facility

500000 + 25*x = 800000 + 22x

3*x=300000

x=100000

for 100,000 units total cost will be equal

c) For site 1 to be superior the range of unit should be less than 100,000.

d) For site 2 to be superior the range of units should be more than 100,000.

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