If the cost function and revenue function of x units of an item are given by \(C(x)=25x^2-x\) and \(R(x)=4x\). Then the number of items to be produced to have maximum profit is,
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{1}{10}\)
Profit = revenue − cost:
\(P(x) = 4x - (25x^2 - x)\)
\(= 5x - 25x^2\)
For a maximum, \(P'(x) = 0\):
\(P'(x) = 5 - 50x = 0\)
\( \displaystyle x = \frac{1}{10} \)
Since \(P''(x) = -50 \lt 0\), this is a maximum.