effort
Senior Member
USA
38 Posts 
Posted  09/09/2013 : 11:39:29

A builder intends to construct a storage shed having a volume of V ft, a flat roof, and a rectangular base whose width is threefourths the length. the cost per square foot of the material is $4 for the floor, $6 for the sides, and $3 for the roof. What dimensions will minimize the builder's cost?
[blue]Here is what I have so far but now I am stuck. Will someone check my work and show me how to finish solving this?[blue]
area of floor= 4wl, shed has 4 sides, 2 with area length times height and 2 with area width times height. so the cost of the material is 6lh and 6(2wh). the cost of the roof is 3wl.
Cost = 4(L)(3L/4)+ 3(L)(3L/4) + 6*2(L + 3L/4)h = 3L + 9L/4 +21Lh = 21L/4 + 21Lh Now I know I am suppose to sub in a valus for a variable and then differentiate but I don't have a value to use to sub in. So I can't find the dimensions. Will someone show me how to finish this problem? 

