If the total cost and total revenue of a company that produces and sells \(x\) units of a particular product are \(C(x)=5x+350\) and \(R(x) = 50x-x^2\) respectively, then which of the following is/are the breakeven values:
(A) \(x = 10\)
(B) \(x = 25\)
(C) \(x = 45\)
(D) \(x = 30\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) only
At the break-even point, revenue equals cost:
\( \displaystyle 50x - x^2 = 5x + 350 \)
\( \displaystyle x^2 - 45x + 350 = 0 \)
\( \displaystyle (x - 10)(x - 35) = 0 \)
So the break-even values are \(x = 10\) and \(x = 35\).
Checking the statements
(A) \(x = 10\) — Correct. \(C(10) = 400\) and \(R(10) = 500 - 100 = 400\).
(B) \(x = 25\) — Incorrect. \(C(25) = 475\), but \(R(25) = 625\).
(C) \(x = 45\) — Incorrect. \(C(45) = 575\), but \(R(45) = 225\).
(D) \(x = 30\) — Incorrect. \(C(30) = 500\), but \(R(30) = 600\).