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Sagot :
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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