Question

Calc Problem Need Help!

A postal service will accept packages only if the length plus girth is no more than 60 inches. (See the figure.) Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept?
in^3=?

not sure how to find the max with girth :/

Answer 1

would it be v"=120x-24x

Answer 2

The length plus girth can't be more than 60 inches. Therefore, for a given length L, the girth must be 60-L. Since the front is square, the sides are the same length, thus the face dimensions are 60-L * 60-L. Multiply that by the length L to get volume:

L * 60-L * 60-L
= L^3 - 120L^2 + 3600L

To maximize, you differentiate and set it to 0:
3L^2 - 240L + 3600 = 0
L=20 or 60

60 is a degenerate answer, so the solution is L=20, meaning max volume comes from a 20x40x40 box.

Answer 3

hello?

Answer 4

not sure thats the right answer

Answer 5

explain

Answer 6

so the max volume is 20x40x40 not sure what that means

Answer 7

the largest volume is attained when the dimensions are 20x40x40. The length and girth are 20 and 40, which adds up to 60, the limit.

Answer 8

i need to find the max volume in cubic inches

Answer 9

okay so that's 20*40*40 which is 32000

Answer 10

thats wat i thought haha

Answer 11

i assume this is calculus class?

Answer 12

but im i dont think ur solution is right

Answer 13

okay, howcome?

Answer 14

you might need to draw the figure referenced in the problem