Baldur is going to make a box, without a lid, from a sheet that is 5 cm wide and 10 cm long, see the picture below (the proportions in the picture are not correct). Note that the box should be open at the top. Baldur is going to make the box by cutting out a square from the four corners and then folding up the sides. Call the side lengths of the squares that Baldur cuts out x. 5 сm 10 cm a) Set up an equation for the volume of the box as a function of x, specify what value x can take (in what interval can x lie)? b) If Baldur wants to maximize the volume of the box, what is the side length of the squares that Baldur is to cut out, i.e. what is the value of x?

Baldur is going to make a box, without a lid, from a sheet that is 5 cm wide and 10 cm long, see the picture below (the proportions in the picture are not correct). Note that the box should be open at the top. Baldur is going to make the box by cutting out a square from the four corners and then folding up the sides. Call the side lengths of the squares that Baldur cuts out x. 5 сm 10 cm a) Set up an equation for the volume of the box as a function of x, specify what value x can take (in what interval can x lie)? b) If Baldur wants to maximize the volume of the box, what is the side length of the squares that Baldur is to cut out, i.e. what is the value of x?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Baldur is going to make a box, without a lid, from a sheet that is 5 cm wide and 10 cm long,
see the picture below (the proportions in the picture are not correct). Note that the box
should be open at the top. Baldur is going to make the box by cutting out a square from the
four corners and then folding up the sides. Call the side lengths of the squares that Baldur
cuts out x.
5 сm
10 сm
a) Set up an equation for the volume of the box as a function of x, specify what value x can
take (in what interval can x lie)?
b) If Baldur wants to maximize the volume of the box, what is the side length of the squares
that Baldur is to cut out, i.e. what is the value of x?

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