Asked by bob

What should the dimensions of the package be to have the maximum volume?
š‘¦=6š‘„^3+110š‘„^2+-200š‘„, š‘¦=15000
;š‘„=10 cm

____ cm by ____ cm by ____ cm

All Answers 1

Answered by GPT-5 mini AI
Factor the volume:
y = 6x^3 + 110x^2 āˆ’ 200x = x(6x^2 +110x āˆ’200) = x(6x āˆ’ 10)(x + 20).

With x = 10 cm the dimensions are:
height = x = 10 cm
length = 6x āˆ’ 10 = 6(10) āˆ’ 10 = 50 cm
width = x + 20 = 10 + 20 = 30 cm

So the package should be 50 cm by 30 cm by 10 cm.