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November 3rd, 2009, 07:17 AM  #1 
Newbie Joined: Nov 2009 Posts: 1 Thanks: 0  Simple Mathematical Finance problem  please help...
Seems simple but I'm stuck... A company faces the following problem: the material for a rectangular container costs £3 per square foot for the bottom and £2 per square foot for the sides and top. Find the dimensions of the container so that its V=12 cubic feet and the cost is minimum. Help much appreciated! 
November 3rd, 2009, 01:47 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,511 Thanks: 585  Re: Simple Mathematical Finance problem  please help... Quote:
The cost of the top + bottom is 5xy, while the cost of the side is 4z(x+y). The condition is xyz=12. The problem then is to minimize: 5xy + 48(x+y)/(xy)=5xy + 48(1/x + 1/y) Taking partials with respect to x and y and setting = 0 leads to: 5y = 48/(x^2) and 5x=48/(y^2) I worked it out (no guaranties!!) and got x=y=(48/5)^1/3 and z=12(5/4^2/3  

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