Solve the problem.
-A rectangular piece of cardboard measuring 30 inches by 50 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let $x$ represent the length of a side of each such square. For what value of $x$ will the volume be a maximum? If necessary, round to 2 decimal places.
A) $20.6$ in.
B) $6.07 \mathrm { in }$.
C) $25 \mathrm { in }$.
D) $41.2$ in.

Question

Quizplus · Accepted Answer

The volume of the box, $V$, formed by cutting out squares of side $x$ and folding up the sides is given by $V = x(30 - 2x)(50 - 2x)$. To find the value of $x$ that maximizes $V$, we differentiate $V$ with respect to $x$ and set the derivative equal to zero. Solving this gives $x \approx 6.07$ inches.

Solve the Problem xxx Represent the Length of a Side of Each Such Square

Solve the Problem $x$ Represent the Length of a Side of Each Such Square