ANSWER
The correct answer is D
EXPLANATION
To graph the inequality
[tex]x+3y\le 6[/tex]
we first graph the corresponding equation,
[tex]x+3y= 6[/tex]
We then test the origin to determine which half-plane to shade the inequality,
[tex]0+3(0)\le 6[/tex]
[tex]0\le 6[/tex]
The above statement is true so we shade the lower half plane.
Next, we graph
[tex]4x+6y\ge 9[/tex]
By first graphing the corresponding equation,
[tex]4x+6y=9[/tex]
Then we test the origin again,
[tex]4(0)+6(0)\ge 9[/tex]
[tex]0\ge 9[/tex]
This statement is false, so we shade the upper half plane
Next, we graph,
[tex]x\ge 0[/tex]
Draw the vertical line [tex]x=0[/tex] and shade to the right.
Finally, we graph,
[tex]y\ge 0[/tex]
Draw the horizontal line [tex]y=0[/tex] and shade the upper region.
the intersection of all the shaded regions is called the feasible region.
The four vertices of the feasible region are
[tex](0,\frac{3}{2}),(0,2),(6,0),( \frac{9}{4},0)[/tex]
Hence the correct answer is D
