Mathematics: 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?

AMark brainliest please Hope this helps you...

Suppose an airline policy states that all baggage

QueenNerdy889

30.01.2022

140608 cubic in

Step-by-step 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

$V^{\prime}=312x-6 x^{2} \quad<img src=$ V=0" alt=" When" />V=0" />

$312x-6 x^{2}=0$

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

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

$V=52\times52\times52= 140608 \text{ cubic in}$

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