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If cost is represented by [tex]C(x) = 7.6x + 82,000[/tex] and revenues are represented by [tex]R(x) = 10.2x[/tex], which equation could be used to find the break-even point?

Select the correct answer below:

A. [tex]10.2x = 7.6x + 82,000[/tex]
B. [tex]-10.2x = 7.6x + 82,000[/tex]
C. [tex]10.2x = 7.6x - 82,000[/tex]
D. [tex]17.8x = 82,000[/tex]
E. [tex]17.8x = 7.6x + 82,000[/tex]

Answer :

To find the break-even point, we need to set the cost equal to the revenue. The cost function, [tex]\(C(x)\)[/tex], and the revenue function, [tex]\(R(x)\)[/tex], are provided:

- The cost function is [tex]\(C(x) = 7.6x + 82,000\)[/tex].
- The revenue function is [tex]\(R(x) = 10.2x\)[/tex].

To find the break-even point, set these two expressions equal to each other:

[tex]\[ R(x) = C(x) \][/tex]

This means:

[tex]\[ 10.2x = 7.6x + 82,000 \][/tex]

This equation represents the condition where the revenues equal the costs, which is the definition of the break-even point. Therefore, the correct equation to find the break-even point is:

[tex]\[ 10.2x = 7.6x + 82,000 \][/tex]

The correct answer is:

[tex]\[ 10.2x = 7.6x + 82,000 \][/tex]

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