The maximum value of z = 5x + 2y, subject to the constraints $x+y\le 7,x+2y\le 10,x,y\ge 0$ is 

Change the inequalities into equations and draw the graph oflines, thus we get the required feasible region. The region bounded by the vertices 

$\mathrm{A}(0,5),\mathrm{B}(4,3),\mathrm{C}(7,0)$

The objective function is maximum at C(7,0) and

Max  z $=5\times 7+2\times 0=35$ .