Question

The design of a digital box camera maximize the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what would the dimension be ?
PLEASE help!!!

Answer 1

Hint: let x represent one of the dimensions, and then define the other dimensions in terms of x

Answer 2

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Answer 3

Let L, W and H be the dimensions
L = 1.5 * H
L + W + H = 6
Volume V = LWH
Find L and W in terms of H from the first two equations, put it in the V.
To maximize V, find dV/dH and set it to 0 and solve for H
Substitute in the first two equations and find L and W

Answer 4

Thank you!

Answer 5

you are welcome.