Find the Minimum and Maximum Values of the Objective Function $z = 2 x + 8 y$

Multiple Choice

Find the minimum and maximum values of the objective function $z = 2 x + 8 y$ and where they occur, subject to the constraints $$x \geq 0 , y \geq 0,2 x + y \leq 4$$ .

A) The minimum value is 0 at $( 0,0 )$ and the maximum value is 32 at $( 0,4 )$ .
B) The minimum value is 0 at $( 0,2 )$ and the maximum value is 32 at $( 0,4 )$ .
C) The minimum value is 0 at $( 0,0 )$ and the maximum value is 32 at $( 0,2 )$ .
D) The minimum value is 0 at $( 0,4 )$ and the maximum value is 32 at $( 0,2 )$ .
E) The minimum value is 0 at $( 0,4 )$ and the maximum value is 32 at $( 0,0 )$ .