winterblanco
19.11.2019 •
Mathematics
A. the u.s. postal service will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 in. what dimensions will give a box with a square end the largest possible volume? b. graph the volume of a 108-in. box (length plus girth equals 108 in.) as a function of its length and compare what you see with your answer in part (a).
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Ответ:
The dimensions are 18 * 18 * 36in
Step-by-step explanation:
Let the lengths of the square ends be x in and the length be y in.
Then the maximum length + girth
= 4x + y = 108in
The volume V = x^2y.
From the first equation:
y = 108 - 4x
so V = x^2(108 - 4x)
= 108x^2 - 4x^3
Finding the derivative:
V' = 216x - 12x^2 = 0 ( for a maximum volume).
12x( 18 - x) = 0
x = 18
So the value for x for a maximum volume = 18 in
This gives y = 108 - 4(18) = 36 in.
Ответ: