Q21 of 29 Page 1

If a 20-year-old girl drives her car at 25 km/h, she has to spend Rs 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs 5/km. She has Rs 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem.

Let the distance covered at 25km/h be ‘x’ km and distance covered at 40 km/h be ‘y’ km


We have to maximize distance i.e. Z = 25x + 40y


Given, Total amount = 200 Rs


Rate of petrol at 25km/h = Rs 4/km


Rate of petrol at 40km/h = Rs 5/km


⇒ 4x + 5y = 200



Also, as distance is always positive


We have, x ≥ 0 and y ≥ 0


Let the plot the region on graph,



Now,



Therefore, value is maximum at (0, 30), therefore she should travel 30 km at 40km/h


Value shown: Sustainable use of petrol so that future generation can also avail the use of petrol.


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