Solve the problem.
-A rectangular box with volume 268 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) $C ( x ) = 3 x ^ { 2 } + \frac { 1072 } { x }$
B) $C ( x ) = 3 x ^ { 2 } + \frac { 2144 } { x }$
C) $C ( x ) = 2 x ^ { 2 } + \frac { 2144 } { x }$
D) $C ( x ) = 4 x + \frac { 2144 } { x ^ { 2 } }$

Question

Solve the problem.
-A rectangular box with volume 268 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) $C ( x ) = 3 x ^ { 2 } + \frac { 1072 } { x }$
B) $C ( x ) = 3 x ^ { 2 } + \frac { 2144 } { x }$
C) $C ( x ) = 2 x ^ { 2 } + \frac { 2144 } { x }$
D) $C ( x ) = 4 x + \frac { 2144 } { x ^ { 2 } }$

Quizplus · Accepted Answer

The cost function is derived by calculating the cost of the top and bottom as $2 \times 1.5 \times x^2 = 3x^2$ and the cost of the sides as $4 \times 2 \times \frac{268}{x} = \frac{2144}{x}$. Thus, the total cost function is $C(x) = 3x^2 + \frac{2144}{x}$.

Solve the Problem C(x)=3x2+1072xC ( x ) = 3 x ^ { 2 } + \frac { 1072 } { x }C(x)=3x2+x1072​

Solve the Problem $C ( x ) = 3 x ^ { 2 } + \frac { 1072 } { x }$