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

Asked by Topperlearning User 4th June 2014, 1:23 PM

Suppose the man sides x km at 25 km per hour and y km at 40 km per hour.
Thus, we have following LPP
Maximum z = x + y
st 2x+ 5y  100
8x + 5y  200
x  0, y  0

 Corner Points Z = x + y O(0, 0) A(25, 0) B C(0, 20) z = 0 z = 25 z =  = 30 z = 20

Maximum z is 30 if , y =
Hence, young man cover the maximum distance of 30 km if he sides  km at 25 km/hr and  at 40 km/hr

Answered by Expert 4th June 2014, 3:23 PM
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