Let x = distance (km) travelled at 50 km/h and y = distance (km) travelled at 80 km/h.
Maximise Z = x + y
Subject to:
- Petrol cost: 2x + 3y ≤ 120
- Time: x/50 + y/80 ≤ 1, which simplifies to 8x + 5y ≤ 400
- x ≥ 0, y ≥ 0
(Multiplying x/50 + y/80 ≤ 1 by 400 gives 8x + 5y ≤ 400.)
Identity