Hyundai Motors is considering three sites A$,$ B$,$ and C at which to locate a factory to build its new electric car batteries. 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

Annualized Fixed Cost

A $-$ $$10,000$

B $-$ $$24,000$

C $-$ $$27,000$

Variable Cost per Battery Produced

A $-$ $$2,400$

B $-$ $$1,900$

C $-$ $$1,050$

The firm knows it will produce between $0$ and $60,000$ batteries at the new plant each year, but, thus far, that is the extent of its knowledge about production plans.

Part $2$

a$)$ The value of volume, V$,$ of production above which site C is recommended $=$

$$

batteries $($round your response up to the next whole number$).$

Part $3$

b$)$ The value of volume, V$,$ of production below which site A is recommended $=$

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enter your response here batteries $($round your response up to the next whole number$).$

Part $4$

c$)$ Over what range of volume is site B optimal?

A$.$

Site B is never optimal because its cost line always exceeds that of A or C for all volume levels.

B$.$

Site B is optimal for volumes from $12,593$ to $28,000$ batteries.

C$.$

Site B is optimal for volumes above $28,000$ batteries.

D$.$

Site B is always optimal because its cost line is always below that of A and C for all volume levels.