Question

the u.s post office will accept a box for shipment only if the sum of the length and girth (distance around) is at most 108 inches. Find the dimensions of the largest acceptable box with

Answer 1

Answer:

The dimension of the largest acceptable box

$18in\times 18 in\times 36 in$

Step-by-step explanation:

Let length of box,l=x

Side of square base=y

We are given that

x+4y=108

$x=108-4y$

Now, volume of box,V=$x^2 h=y^2x=y^2(108-4y)=108y^2-4y^3$

$\frac{dV}{dy}=216y-12y^2$

$\frac{d^2V}{dy^2}=216-24y$

$\frac{dV}{dy}=0$

$216y-12y^2=0$

$12y(18-y)=0$

$y=0,18$

y=0 is not possible

Therefore, y=18

$\frac{d^2V}{dy^2}=216-24(18)<0$

Hence, the volume of box is maximum when y=18

Now, $x=108-4(18)=36 in$

Hence, the dimension of the largest acceptable box

$18in\times 18 in\times 36 in$

Answer 2

Answer:

18in* 18in* 36in

Step-by-step explanation: