A bulldozer manufacturer produces x items and the total cost C and total revenue R are given by $C= 100 +0.015x^2$ and R =3x. The number of bulldozers to be produced for maximum profit is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100
Profit (P) is,
$P(x)=R(x)-C(x)$
$=3x-(100+0.015x^2)$
$=-0.015x^2+3x-100$
$\frac{dP}{dx}=-0.03x+3$
$=-0.03x+3=0$
$=x=100$ → Maxima occurs.