Which of these pairs of costs and revenues could a company have if it's at its break-even point?

A. Costs of [tex]$5000[/tex] and revenues of [tex]$7000[/tex]
B. Costs of [tex]$5000[/tex] and revenues of [tex]$6000[/tex]
C. Costs of [tex]$6000[/tex] and revenues of [tex]$6000[/tex]
D. Costs of [tex]$6000[/tex] and revenues of [tex]$7000[/tex]

To find the break-even point, we need to determine when the company's costs equal its revenues. This means we are looking for the pair where

[tex]$$
\text{cost} = \text{revenue}.
$$[/tex]

Let's analyze each option:

1. Option A:
Costs: [tex]$\$[/tex]5000[tex]$, Revenue: $[/tex]\[tex]$7000$[/tex]
Since [tex]$\$[/tex]5000 \neq \[tex]$7000$[/tex], this option is not at break-even.

2. Option B:
Costs: [tex]$\$[/tex]5000[tex]$, Revenue: $[/tex]\[tex]$6000$[/tex]
Since [tex]$\$[/tex]5000 \neq \[tex]$6000$[/tex], this option is not at break-even.

3. Option C:
Costs: [tex]$\$[/tex]6000[tex]$, Revenue: $[/tex]\[tex]$6000$[/tex]
Since [tex]$\$[/tex]6000 = \[tex]$6000$[/tex], this option is exactly at break-even.

4. Option D:
Costs: [tex]$\$[/tex]6000[tex]$, Revenue: $[/tex]\[tex]$7000$[/tex]
Since [tex]$\$[/tex]6000 \neq \[tex]$7000$[/tex], this option is not at break-even.

Since the break-even condition [tex]$\text{cost} = \text{revenue}$[/tex] is only satisfied in Option C, the company is at its break-even point when it has costs of [tex]$\$[/tex]6000[tex]$ and revenues of $[/tex]\[tex]$6000$[/tex].

Thus, the correct answer is Option C.