Question

Please help me work through 2, thank you! (the answer previously put there was incorrect) thank you!

Answer 1

See below

Explanation:

L will be 14 -2x W will be 11-2x and H will be x

Volume = L * W * H = (14-2x)(11-2x)(x) = 4x^3 - 50x^2 + 154x

Graphing this shows max volume of 140.039 in^3

when x = 2.039

Answer 2

Given:

Find-:

The maximum possible volume of this box

Explanation-:

For maximum possible volume,

So, volume is:

`V(x)=x(14-2x)(11-2x)`

For maximum volume:

`\begin{gathered} V(x)=x(154-28x-22x+4x^2) \\ \\ V(x)=x(4x^2-50x+154) \\ \\ V(x)=4x^3-50x^2+154x \end{gathered}`

Graph of function:

Maximum is:

`(x,f(x))=(2.039,14.039)`

So the maximum possible volume is 14.039