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]
- 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]
