# Math Help - Optimization problem. Can u help?

1. ## Optimization problem. Can u help?

Can anyone help? Here's the problem:

Optimization Problem.

Here's the question:
A box with open top is to be constracted from a square piece of cardboard 3feet wide,by cutting out a square from each of the corners and bending up the sides. Find the largest volume that sucha box can have.
a) Picture: Draw a diagram illustrating the general situation.
b) Objective: Write an expression representing the volume fo the resulting box.
c) Help: Make sure that the objective is entirely in terms of one variable, x.
d) Maximize or Minimize: Find the critical points of the object.
e) Prove it: Use the closed interval domain check, the 1st derivative or the 2nd derivative test. ( pos says min, neg says max)
f) Answer the question: Use the variable solution to answer the particular problem's question.

2. cut four squares of size x by x from each corner, then fold up the flaps.

resulting 3D box dimensions are (3-2x) by (3-2x) by x

$V = x(3-2x)^2$

that's the difficult part ... do the calculus and find the value of x that will maximize the volume.

remember your usable domain ... 0 < x < 3