Solve the problem.
-A rectangular box with volume 433 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the
Base. Express the cost the box as a function of x.
A) $C ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }$
B) $C ( x ) = 4 x + \frac { 3,464 } { x ^ { 2 } }$
C) $C ( x ) = 3 x ^ { 2 } + \frac { 1,732 } { x }$
D) $C ( x ) = 2 x ^ { 2 } + \frac { 3,464 } { x }$

Question

Quizplus · Accepted Answer

The cost function $C(x)$ combines the cost of the top and bottom, which is $2 \times 1.50x^2 = 3x^2$, with the cost of the sides. The volume is $x^2h = 433$, so $h = \frac{433}{x^2}$. The area of the four sides is $4xh = 4x \times \frac{433}{x^2} = \frac{1732}{x}$, and at $2.00 per square foot, the cost for the sides is $2 \times \frac{1732}{x} = \frac{3464}{x}$. Thus, $C(x) = 3x^2 + \frac{3464}{x}$.

Solve the Problem C(x)=3x2+3,464xC ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }C(x)=3x2+x3,464​

Solve the Problem $C ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }$