If the cost function and profit function for a company is given by \(C=10-0.3x^2\) and \(P=0.3x^2+2x-10\) respectively, where \(x\) represents units of output.
The revenue function is given by :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(2x\)
Profit = Revenue − Cost, so the revenue is profit plus cost:
\(R = P + C\)
\(R = (0.3x^2 + 2x - 10) + (10 - 0.3x^2)\)
\(R = 2x\)
Why the other options are incorrect
Option (2) \(-2x\) — Incorrect. This is \(-(P + C)\), the sign is wrong; revenue from a positive output cannot be negative.
Option (3) \(20-0.6x^2-2x\) — Incorrect. This is C − P, cost minus profit; the revenue is P + C.
Option (4) cannot be determined — Incorrect. Both P and C are given, and R = P + C = 2x.