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July 24th, 2014, 04:45 PM  #1 
Newbie Joined: Jul 2014 From: ontario Posts: 6 Thanks: 0  determine the dimensions of the box with maximum volume
a box with an open top is to be made from a piece of cardboard with dimensions 60cm by 90cm by cutting a square from each corner and them folding up the sides. if the cut must be at least 5cm, determine the dimensions of the box with maximum volume? please help me i don't what to do thanks so much 
July 25th, 2014, 01:49 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 732 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
1. Draw a diagram and label some of the important information with numbers or algebraic labels, such as the lengths of the sides of the box when it is opened up as a net. 2. Find a formula that describes the volume of the box. It will have letters in it because you don't know all the information. 3. i) We want to find the maximum volume. Well... if we change the unknown parameters, we get different volumes of the box. A long thin box has a smaller volume than a fat box, right? Therefore, there must be some choice of unknown parameters that gives us the box we want, i.e. the box with the biggest volume. 3. ii) So... we will need a mathematical technique that allows us to get the maximum of a function. Have you studied this yet? (hint: differentiation) Give it a go and let me know how it goes. If you can, attach a diagram to the post too. If you're still puzzled I can give more info. 

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