a delivery company accepts rectangular boxes the sum of whose length and girth (perimeter of a cross-section) does not exceed 108 in. find the dimensions of an acceptable boc

The dimensions of an acceptable box is 18 x 36 inches.

If the package has a combined length and girth of 108 inches. We can determine that:

4x + y = 108

We are also assuming that the cross section is square, so:

V = x²y

Let’s solve for y in the first equation and plug it in to the second equation:

y = 108- 4x

V = x²(108- 4x)

V = 108x² – 4x³

In order to solve for the maximum is when V’ = 0

V’ =216x – 12x² = 0

x(216- 12x) = 0

Therefore, we have 2 solutions,

x = 0

216- 12x = 0

12x = 216

x = 18

x = 0 is when the package is a minimum, so the maximum occurs when x = 18. Now let’s solve for y

y = 108- 4x = 108- 4(18) = 36

The answers are:

x = 18 inches

y = 36 inches

Therefore, the dimensions of an acceptable box is 18 x 36 inches.

dimensions of an acceptable boxis 18 x 36 inches.a combined length and girthof 108 inches. We can determine that:dimensions of an acceptable boxis 18 x 36 inches.perimeterrefer here#SPJ4