12. The cross-section of a triangular prism is an equilateral triangle with side $2 x \mathrm {~cm}$. The length of the prism is $d \mathrm {~cm}$.
Let the total surface area of the prism be $T \mathrm {~cm} ^ { 2 }$. Given that the volume of the prism is $T \mathrm { cm } ^ { 3 }$, which one of the following is an expression for $d$ in terms of $x$ ?
A $\frac { x } { 2 x - 3 }$
B $\frac { 3 x } { 3 x - 2 \sqrt { 3 } }$
C $\frac { 2 x } { x - 4 \sqrt { 3 } }$
D $\frac { 2 x } { x - 2 \sqrt { 3 } }$
E $\frac { 2 x } { x - \sqrt { 3 } }$

An internet company can serve at most 1000 customers and can reach this number when it sets the monthly internet fee at 40 TL. The company has observed that after each 5 TL increase in the monthly internet fee, the number of customers decreases by 50.
At what monthly internet fee should this company set its rate to maximize the total revenue from the monthly internet fee?
A) 55 B) 60 C) 65 D) 70 E) 75

The amount of fuel consumed in 1 hour by a rocket moving at a constant speed of $V$ kilometers per hour is calculated by the function
$$f ( V ) = \frac { V ^ { 3 } } { 20 } - 7 \cdot V ^ { 2 } + 265 \cdot V$$
in units.
Accordingly, what is the minimum amount of fuel in units that this rocket must consume to travel 100 kilometers at a constant speed?
A) 1000
B) 2000
C) 3000
D) 4000
E) 5000

In the rectangular coordinate plane, the shaded region between the lines $y = 2 + 3x$ and $y = 12 - x$ and the positive $x$ and $y$-axes is given below.
Rectangles are constructed in this region with one side on the $x$-axis and one vertex each on the lines $y = 2 + 3x$ and $y = 12 - x$.
What is the length of the side on the $x$-axis of the rectangle with the largest area?
A) 6 B) $\dfrac{19}{3}$ C) $\dfrac{20}{3}$ D) 7 E) $\dfrac{22}{3}$