Find a formula C(x, y, z) that gives the cost of materials for the closed rectangular box, with dimensions in feet. Assume that the material for the top and bottom costs $3 per square

Question

Find a formula C(x, y, z) that gives the cost of materials for the closed rectangular box, with dimensions in feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $6 per square foot

Answer 1

Need the surface area of the box weighted by the costs of the materials.

Let x and y be the base dimensions and z be the height of the box.

Cost of surface area = 3 (top+bottom) + 6 (front+back+left side+right side)

C(x,y,z) = 3(2xy) +6 (xz+xz+yz+yz)

=6xy +6(2xz +2yz)

=6xy +12xz+12yz