Explanation

(d)
Feasible region is $ABCDEA$ and $z = x + 2y$
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At point $A\left( \frac{2}{5},\ 0 \right),\ \ z = \frac{2}{5} + 0 = \frac{2}{5}$
At point $B(6,\ 0),\ \ \ \ \ \ \ z = 6 + 0 = 6$
At point $C(6,\ 7),\ \ \ \ z = 6 + 14 = 20$
At point $D(0,\ 7),\ \ \ z = 0 + 2(7) = 14$
At point $E\left( 0,\frac{1}{2} \right),\ \ \ \ z = 0 + 2\left( \frac{1}{2} \right) = 1$
$\therefore$ The maximum value of $z$ is 20