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If a young man rides his motorcycle at 25 km/hr, he had to spend Rs.2 per km on petrol. If he rides at a faster speed of 40 km/hr, the petrol cost increases at Rs.5 per km. He has Rs.100 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this as LPP and solve it graphically.

1 Answer

Let the young man ride with the speed 25 km/hr for hours and with the speed 40 km/hr for y hours respectively.

Money spent at speed 25 km/hr = 50x
And Money spent at speed 40 km/hr = 200y

Maximum distance :
Z = 25x + 40y        ….(1)

subject to the constraints
x + y ≤ 1               ….(2)
50x + 200y ≤ 100   ….(3)
x , y ≥ 0                ….(4)

Graph the inequalities (2) to (4). The feasible region (shaded) is shown as below:

Corner Point

Z = 25x + 40y

A (0, 1/2)


B (2/3, 1/3)


C(1, 0)


Thus, the maximum distance he can travel is30 km.

answered Mar 17, 2015 by krishvlk

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