We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to

Question

We want to construct a box whose base length is 3 times the base width.  The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2.  If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to

anonymous · Answer

AB = 3w*w    area,base
TB=2*3*w^2       Total base area
SA= 2*3w*x+w*x*2        side areas all 4
50=3w*2*x                 eq for volume
price  =  10/AB

price  =  6/SA           for side areas

hold on i'll work it out :)