Anyone know how to solve this problem?

V = [(8 - 2x)/2] (7 - 2x) x

= (4-x)(7 - 2x) x = (28 - 8x - 7x + 2x^2) x

= 2x^3 - 15x^2 + 28x

dV/dX = 6x^2 - 30x + 28 = 0

Dividing through by 2, we get 3x^2 - 15x + 14 = 0

x =

15 +/- SQRT[225 - 4(3)(14)]
--------------------------------- =
6

15 +/- SQRT(225 - 168)
---------------------------- =
6

15 +/- SQRT(57)
-------------------- =
6

15 +/- 7.55
-------------- = 3.76, 1.24
6

Since 3.76 is too large for the side of size 7, the answer is 1.24.
It gives a box of 2.76 x 4.52 x 1.24 = 15.47.

Function for volume
It looks like the resulting box will have the following dimensions:

Height = X
Width = 7 - 2X
Length = (8-2X)/2

so... volume = X(7-2X)(4-X) = 2x^3 - 15x^2 +28x

Find the maximum of that function either by taking the derivative and solving or by graphing the function and seeing where the maximum is.

Once you find V in terms of x, it's just a standard exercise in maximization.

thax for all ur help.