Asha Joshi - M.Sc. (Mathematics) | Former Faculty at Vedantu (5 Years) & Doon International School (6 Years)

Let $x$x be the distance (in km) travelled at 50 km/hour and $y$y be the distance (in km) travelled at 80 km/hour.

1. Objective function

The total distance travelled is $x+y$x+y.

Since he wants to travel the maximum distance, the objective function is

2. Constraints

Petrol cost constraint:

At 50 km/hour, the cost is Rs 2 per km, and at 80 km/hour, it is Rs 3 per km. The total petrol budget is at most Rs 120.

Time constraint:

Time taken at 50 km/hour is $\frac{x}{50}$50x hours, and at 80 km/hour is $\frac{y}{80}$80y hours. The total time available is at most 1 hour.

Multiplying by 400 gives

Non-negativity constraints:

Final answer: Linear Programming Problem (LPP)

Maximize

Subject to the constraints