In the Linear Programming Problem (LPP), find the point/points giving maximum value for Z =5 x +10 y subject to constraints x +2 y ≤ 120; x + y ≥ 60;…

The corner points of the feasible region are \(\displaystyle (60,0)\), \(\displaystyle (120,0)\), \(\displaystyle (60,30)\) and \(\displaystyle (40,20)\). Evaluating \(\displaystyle Z=5x+10y\): \[\begin{array}{ll} (60,0): & Z=300 \\ (120,0): & Z=600 \\ (60,30): & Z=600 \\ (40,20): & Z=400 \end{array} \] Maximum value \(\displaystyle Z=600\), attained at \(\displaystyle (120,0)\) and \(\displaystyle (60,30)\) — hence at every point on the line segment joining them.