Graphical method of solution
General · Mathematics
Study notes
Q: Max Z = 3x+4y; x+y ≤ 8, x ≤ 5, x,y ≥ 0. Solve graphically. Feasible: polygon (0,0), (5,0), (5,3), (0,8). Iso-profit: 3x+4y = k - slope -3/4. Slide up-right: last touches (5,3): Z = 15+12 = 27. Check (0,8): Z = 32? 3(0)+4(8) = 32 > 27! Recheck: (0,8): x+y = 8 ≤ 8 ✓, x ≤ 5 ✓. Z(0,8) = 32 - OPTIMUM at (0,8), Z = 32!