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 y: y = 6x^3 + 110x^2 āˆ’ 200x = 2x(x+20)(3xāˆ’5).
So the three dimensions are 2x, x+20, and 3xāˆ’5. For x = 10 cm those are

2(10) = 20 cm, 10+20 = 30 cm, 3(10)āˆ’5 = 25 cm.

Answer: 20 cm by 30 cm by 25 cm.