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Mathematics Clinic => Calculus => Topic started by: vicky on Dec 18, 2021

Title: A private shipping company will accept a box for domestic shipment only if the sum of its length and ...
Post by: vicky on Dec 18, 2021
A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 114 in. Suppose you want to mail a box with square sides so that its dimensions are and it's girth is What dimensions will give the box its largest volume?
◦ 19 in. × 19 in. × 38 in.
◦ in. × in. × 19 in.
◦ 19 in. × 19 in. × 95 in.
◦ 38 in. × 19 in. × 38 in.
Title: A private shipping company will accept a box for domestic shipment only if the sum of its length and ...
Post by: EAN94 on Dec 18, 2021
in. × in. × 19 in.


Length + Girth = ; h + (2h + 2w) = ;  3h + 2w =

Solve for w: w = <> - h
The Volume can be expressed as a function of h by:

V(x)  = h2w = h2(<> - h)

V'(x) = h - h2

Solve V'(x) = 0: h = <>
w = <> - (<>) = <>
The dimensions that give the largest possible volume would be <> x <> x <>