A chocolate manufacturer uses an equilateral triangular prism package. If the volume of chocolate to be contained in the package is 400cm^3, what dimensions of the package will use the minimum amount of materials?
2007-01-06 03:14:49 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
See the following link, where this same question was asked a week ago.
http://answers.yahoo.com/question/index;_ylt=AvykecBfieOYuwF.Rd6qbygjzKIX?qid=20061229230029AAudmEg
2007-01-06 03:16:37 · answer #1 · answered by Jim Burnell 6 · 1⤊ 0⤋
You want to minimize the surface area of the prism, so you need a function for the surface area, find its derivative, set it to zero.
The surface area is the sum of the 2 triangluar bases and the 3 rectangular faces. Let S be the length of the triangle side and H be the height of the rectangular face (the other side of the rectangle is just S).
The problem is that this function for surface area has two variables, S and H, so you need to eliminate one. You need a relationship between S and H. You get that from the fixed volume. The volume is the area of the triangle times the height of the rectangle. Isolate one of the S or H variable and substitue into the surface area function.
Now you can differentiate the surface area, find the zeros, and minimize.
2007-01-06 11:24:32 · answer #2 · answered by grand_nanny 5 · 1⤊ 0⤋
i dont know dude.... like 200 some?
2007-01-06 11:16:46 · answer #3 · answered by Ladywoman 2 · 0⤊ 3⤋
It's in your textbook.
2007-01-06 11:16:41 · answer #4 · answered by Joe S 6 · 0⤊ 3⤋