Hyundai Motors is considering three sites-A, B, and C-at which to locate a factory to build its new-model automobile, the Hyundai Sport C150. The goal is to locate at a minimum cost site, where cost is measured by the annual fixed plus variable costs of production. Hyundai Motors has gathered the following data:
| Site |
Anmualized Fixed Cost |
Variable cost per auto produced |
| A |
$10,000,000 |
$2,500 |
| B |
$20,000,000 |
$2,000 |
| C |
$25,000,000 |
$1,000 |
The firm knows it will produce between 0 and 60,000 Sport C150s at the new plant each year, but, thus far, that is the extent of its knowledge about production plans.
a) For what values of volume, V, of production, if any, is site C a recommended site?
b) What volume indicates site A is optimal?
c) Over what range of volume is site B optimal? Why?