(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Question:

You are planning to make an open rectangular box from a 10 by 18 cm piece of cardboard by cutting congruent squares from the corners and folding up the sides.

1) What are the dimensions of the box of largest volume you can make this way?

2) What is its volume?

v - volume

l - length

h - height

w - width

2. Relevant equations

v = lwh

3. The attempt at a solution

Since v = lwh w = 10 - 2h and l = 18 - 2h.

Therefore:

v(h) = (18-2h)(10-2h)(h)

v(h) = (4h^3) - (56h^2) + 4h^2

Differentiation:

dv/dh = (12h^2) - 112h + 180

Finding critical numbers:

(12h^2) - 112h + 180 = 0

(12h^2) - 112h = -180

h(12h - 112) = -180

12h - 112 = -180

12h = -68

h = -68/12

critical numbers: k{-180, -68/12}

My question is, how can I have a negative height? Is this correct so far or have I made some error?

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# Homework Help: Box Optimization problem

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