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A postal service says that a rectangular
package can have a maximum combined length
and girth of 108 inches. The girth of a package is the
distance around the perimeter of a face that does not
include the length.
a. Write an inequality that represents the allowable
dimensions for the package.
b. Find three different sets of allowable dimensions that are
reasonable for the package. Find the volume of each package.
girth

Sagot :

MrRoyalidn

The volume of the rectangular package is the amount of space in the package

  • The inequality that represents allowable dimensions is 4x + y ≤ P
  • Three possible dimensions are: 2 by 100,1 by 104 and 1.5 by 102

The inequality that represents allowable dimensions

Let the dimension of the package be x and y.

So, the perimeter (P) and the volume (V) are

P = 4x + y

V = x²y

The maximum perimeter of the box is P.

So, the inequality is:

4x + y ≤ P

The three different dimensions

Recall that:

P = 4x + y

The perimeter becomes

4x + y = 108

Make y the subject

y = 108 - 4x

Substitute y = 108 - 4x in V = x²y

V = x²(108 - 4x)

Expand

V = 108x² - 432x

Differentiate

V' = 216x - 432

Set to 0

216x - 432 = 0

Add 432 to both sides

216x = 432

Divide by 216

x = 2

Substitute x = 2 in y = 108 - 4x

y = 108 - 4 * 2

Evaluate

y = 100

So, the inequalities are:

x ≤ 2 and y ≤ 100

Using the above inequality, three possible dimensions are: 2 by 100,1 by 104 and 1.5 by 102

Read more about maximum volumes at:

https://brainly.com/question/10373132

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