Question17. The area of a rectangular enclosure is given by the function, $A(x)=-5 x^{2}+150 x$, where $x$ is the width. in meters. What is the width that will produce the maximum area? A) 5 m B) 15 m C) 150 m D) 30 m

Studdy Solution
For the function $A(x) = -5x^2 + 150x$, identify $a = -5$ and $b = 150$.
Substitute into the vertex formula: $$x = -\frac{150}{2(-5)} = \frac{150}{10} = 15$$
The width that will produce the maximum area is:
$$\boxed{15 \text{ m}}$$