Find a formula C (x, y, z) that gives the cost of materials for a 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 $5 per square foot. Show all work in steps clearly.

C (x, y, z) = 6*x*y+10*x*z+10*y*z

Step-by-step explanation:

Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.

x*y

There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.

2*x*y

and the cost is 3$ for per square foot and the cost for top and bottom is:

6*x*y$

Surface areas of side surfaces are multiply of width, height and length, height:

x*z+y*z

There are 4 side surfaces exist. Therefore the are need to be multiply with 2.

2*x*z+2*y*z

and the cost is 5$ for per square foot and the cost for side surfaces is:

10*x*z+10*y*z

Total equality for cost is C (x, y, z) = 6*x*y+10*x*z+10*y*z