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 $2.10 per square foot to build the base and $0.75 per square foot to build the Sides. Write the cost C of constructing the box as a function of x, y, and z.
A) $C = 2.10 x z + 1.50 ( x y + y z )$
B) $C = 2.10 x z + x y + 2.25 y z$
C) $C = 2.10 x y + 1.50 ( x z + y z )$
D) $C = 2.10 x y + 1.50 x z + 0.75 y z$
E) $C = 2.10 x y + 2.25 ( x z + y z )$

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 $2.10 per square foot to build the base and $0.75 per square foot to build the Sides. Write the cost C of constructing the box as a function of x, y, and z. 
A) $C = 2.10 x z + 1.50 ( x y + y z )$
B) $C = 2.10 x z + x y + 2.25 y z$
C) $C = 2.10 x y + 1.50 ( x z + y z )$
D) $C = 2.10 x y + 1.50 x z + 0.75 y z$
E) $C = 2.10 x y + 2.25 ( x z + y z )$

Quizplus · Accepted Answer

The cost of constructing the box includes the cost of the base and the sides. The base has an area of $xy$ square feet and costs $2.10 per square foot, so the cost for the base is $2.10xy$. The sides include two pairs of rectangles: two with dimensions $x \times z$ and two with dimensions $y \times z$, each costing $0.75 per square foot. Therefore, the total cost for the sides is $2 \times 0.75(xz + yz) = 1.50(xz + yz)$. Adding these costs gives the total cost function $C = 2.10xy + 1.50(xz + yz)$.

A Rectangular Box with an Open Top Has a Length C=2.10xz+1.50(xy+yz)C = 2.10 x z + 1.50 ( x y + y z )C=2.10xz+1.50(xy+yz)

A Rectangular Box with an Open Top Has a Length $C = 2.10 x z + 1.50 ( x y + y z )$