How to solve such an optimization problem efficiently？?

How do I solve this Optimization Problem?

• I don't understand anything about optimization. What is the purpose of doing this??? ....I don't understand....(TT_TT). I only know that I need to use the volume and surface area equation, but why? Problem Below: An open rectangular box with square base is to be made from 48 ft^2 of material. What dimensions will result in a box with the largest possible volume?

• Answer:

  Let say you want to make a box for a gift and you want to know the volume before you cut the board. Square base means width*length= a*a=48 ft^2 a=sqrt(48)=9 ft Now to make a box you need to cut squares from the corners so you can fold the side to form the box ( the length of the side of the square is the height of the box) This problem called A Box Folding Problem here the box volume changes in such way it increase as the box height increase then it start to decreases. the optimization question is what is the length squares you need to cut so you get maximum volume in the box here a link to a web page show you the relation http://www.math.washington.edu/~conroy/general/boxanim/boxAnimation.htm here some student work in geogebra in such problems you will enjoy http://www.geogebratube.org/student/m7393 http://www.geogebratube.org/student/m4997 http://answers.yahoo.com/question/index;_ylt=AvSj2fnJZh28_d.sO3vqud4jzKIX;_ylv=3?qid=20120520123214AAfDHTV some links you can find helpful http://answers.yahoo.com/search/search_result;_ylt=AslJAbTWQqvpLSgxlRDCj9UjzKIX;_ylv=3?scope=all&category=396545161&fltr=_en&question_status=all&answer_count=any&date_submitted=all&crumb=SPkvGARN%2FoR&p=A+Box+Folding&orderby=rank&add_save_name=Name+your+search&filter_search=+Apply http://cnx.org/content/m21915/latest/ http://apcalc06.blogspot.com/2006_12_01_archive.html