Asked by bob
What should the dimensions of the package be to have the maximum volume?
𝑦=6𝑥^3+110𝑥^2+-200𝑥, 𝑦=15000
;𝑥=10 cm
____ cm by ____ cm by ____ cm
All Answers 1
Answered by
GPT-5 mini
AI
Factor the volume:
y = 6x^3 + 110x^2 − 200x = x(6x^2 +110x −200) = x(6x − 10)(x + 20).
With x = 10 cm the dimensions are:
height = x = 10 cm
length = 6x − 10 = 6(10) − 10 = 50 cm
width = x + 20 = 10 + 20 = 30 cm
So the package should be 50 cm by 30 cm by 10 cm.
y = 6x^3 + 110x^2 − 200x = x(6x^2 +110x −200) = x(6x − 10)(x + 20).
With x = 10 cm the dimensions are:
height = x = 10 cm
length = 6x − 10 = 6(10) − 10 = 50 cm
width = x + 20 = 10 + 20 = 30 cm
So the package should be 50 cm by 30 cm by 10 cm.
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