A box is constructed of two different types of metal. The metal for the top and bottom which are both square costs $5 per square foot and metal for the sides costs $6 per square ft find the dimensions that minimize cost if the box has a v=25ft.

Question

A box is constructed of two different types of metal.  The metal for the top and bottom which are both square costs $5 per square foot and metal for the sides costs $6 per square ft find the dimensions that minimize cost if the box has a v=25ft.

pfenn1 · Answer

The surface area of a six-sided box = 2 HW + 2HD + 2WD
where H=height of box, D=depth of box, W=width of box.  But because the width and depth are the same (the top and bottom are square) then
Surface area = 4 HW +2 W^2

pfenn1 · Answer

hmmmmm.......what is v?  Is that the width of the box?  the height?

anonymous · Answer

|dw:1335412010307:dw|
so since the base and top are both squares, their lenght n width will be same which we let to be as x. we let the height be y . The are of top n bottom will be 2x^2 and that of the 4 remaining are 4xy, so total are of box will be 2x^2 + 4xy. The cost will thus be 5(2x^2) + 6(4xy)