Solve the Problem $x$ ,
B What Value Of Trough $x$ Will Maximize the Volume of Water That Can Be Carried

Solve the problem.
-A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes
A fold along the two long sides a distance of x inches from the edge.
a. Write a function to represent the volume in terms of $x$ ,
b. What value of $x$ will maximize the volume of water that can be carried by the gutter?

A) a. $V ( x ) = - 2 x ^ { 2 } + 8 x ;$ b. $x = 2$
B) a. $V ( x ) = - 2 x ^ { 2 } + 8 x ;$ b. $x = 1$
C) a. $V ( x ) = - 48 x ^ { 2 } + 192 x$ ; b. $x = 2$
D) a. $V ( x ) = - 48 x ^ { 2 } + 192 x$ ; b. $x = 1$