Question

A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z feet. It costs $4.30 per square foot to build the base and $2.70 per square foot to build the sides. Write the cost C of constructing the box as a function of x, y, and z.

Answer 1

C=$(4.30xy+5.40(xz+yz))

Explanation:

Surface Area of a Cuboid=2(LW+LH+HW)

Since the top is open

Surface Area = LW+2(LH+HW)

If Length = x feet,

Width =y feet

Height = z feet

Surface Area = xy+2(xz+yz)

Area of the base=xy

If it costs $4.30 per square foot to build the base

Cost of the base=Cost Per Square Foot X Area = $4.30xy

Area of the sides =2(xz+yz)

If it costs $2.70 per square foot to build the sides

Cost of the sides=Cost Per Square Foot X Area of the sides

= 2.70 X 2(xz+yz)

=5.40(xz+yz)

Cost of Constructing the Box = Cost of Constructing the Base + Cost of Constructing the Sides.

Therefore,

C=$(4.30xy+5.40(xz+yz))