The corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4), (0, 2)

Now, $\mathit{Z}=5\mathit{x}+7\mathit{y}$
At (0, 0) ; Z = 5(0) + 7(0) = 0
At (7, 0) ; Z = 5(7) + 7(0) = 35
At (3, 4) ; Z = 5(3) + 7(4) = 43
At (0, 2) ; Z = 5(0) + 7(2) = 14
$\therefore {\mathit{Z}}_{\mathit{m}\mathit{a}\mathit{x}}=43$ (at point (3,4))
${\mathit{Z}}_{\mathit{m}\mathit{i}\mathit{n}}=0$ (at point (0, 0))
$\therefore {\mathit{Z}}_{\mathit{m}\mathit{a}\mathit{x}}-{\mathit{Z}}_{\mathit{m}\mathit{i}\mathit{n}}=43-0=43$