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.
a. Write out the equation for total cost for each site.
b. At what volume of output would the two locations have the same total cost?
c. For what range of output would Site 1 be superior?
d. For what range of output would Site 2 be superior?

(a) The equation for the total cost at site 1 is TC = 500,000 + 25X, where X is volume. The equation for total cost at Site 2 is TC = 800,000 + 22X. (b) Set these two equations equal and solve for X. 500,000 + 25X = 800,000 + 22X leads to 300,000 = 3X, then to X = 100,000. (c) Site 1 is preferred for volumes up to 100,000 units, and (d) site 2 is preferred above 100,000 units.