Question

Suppose an airline policy states that all baggage must be​ box-shaped with a sum of​ length, width, and height not exceeding 156 in. What are the dimensions and volume of a​ square-based box with the greatest volume under these​ conditions?

Answer 1

140608 cubic in

Explanation:

`x+x+h=156`

`h=156-2 x`

`V=x^(2) h \quad` We eliminate one of the variables

`V=x^(2)(156-2 x)`

`V=156 x^(2)-2 x^(3)` Differentiating
`v`

`V^(\prime)=312x-6 x^(2) \quad[tex] When`V=0[/tex]

`312x-6 x^(2)=0`

`x(312-6 x)=0 \quad=\quad\left\{\begin{array}{l}x=0 \\ x=52 \quad x=0 \text { not acceptable }\end{array}\right.`

`h=156-2(52)=\Rightarrow h=52`

`V=52*52*52= 140608 \text{ cubic in}`