[RedJoker]

[ QUOTE ]
(1/4)<w<(1/2)
0<x<(1/2)
0<y<(1/2)
0<z<(1/4)

[/ QUOTE ]

The working out:

6w + 6x + 4y + 2z = 5 ............ <font color="red"> Eq 1 </font>
w + x + y + z = 1 ................. <font color="red"> Eq 2 </font>
12w + 8x + 8y + 12z = 10 ...... <font color="red"> Eq 3 </font>

<font color="red"> Eq 1 </font> - 6( <font color="red"> Eq 2 </font>)

-&gt; y = (1 - 4z)/2 ............... <font color="blue"> Eq 4 </font>

<font color="red"> Eq 3 </font> - 2(<font color="red"> Eq 1 </font>)

-&gt; x = 2z ......................... <font color="blue"> Eq 5 </font>

<font color="red"> Eq 3 </font> - 8(<font color="red"> Eq 2 </font>)

-&gt; w = (1 - 2z)/2 ............... <font color="blue"> Eq 6 </font>

From <font color="blue"> Eq 4 </font>:

y &gt; 0
y = (1 - 4z)/2

(1 - 4z)/2 &gt; 0

z &lt; (1/4).................... <font color="green"> Soln 1 </font>

From <font color="blue"> Eq 5 </font>:

x = 2z
z &lt; (1/4)

x &lt; (1/2)............ <font color="green"> Soln 2 </font>

From <font color="blue"> Eq 4 </font>

y = (1 - 4z)/2
z &gt; 0

y &lt; (1 - 4[0])/2

y &lt; (1/2) ....................... <font color="green"> Soln 3 </font>

From <font color="blue"> Eq 6 </font>:

w = (1 - 2z)/2
z &lt; (1/4)

w &gt; (1 - 2[1/4])/2

w &gt; (1/4)

z &gt; 0

w &lt; (1 - 2[0])/2

w &lt; (1/2)

(1/4) &lt; w &lt; (1/2) ........... <font color="green"> Soln 4 </font>