Question

If a $20$ year old girl drives her car at $25km/h$, she has to spend $Rs4/km$ on petrol. If she drives her car at $40km/h$, the petrol cost increases to $Rs5/km$. She has $Rs200$ to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as Linear Programming Problem. Write any one value reflected in the problem.

Answer 1

Let the distance covered with speed of 25kmph be 'x' km

and the distance covered with speed of 40kmph be 'y' km

Total distance covered be 'z' km

The L.P.P of the above problem is

Maximize $z=x+y$

Subject to constraints

$4x+5y\le 200$

$\frac{x}{50}+\frac{y}{40}\le 1$

$x\ge 0,y\ge 0$