8) If John drives a car at a speed of 60 kms/ hour he has to spend Rs. 5 per km on petrol. If he drives at a faster speed of 90 km/hour, the cost of petrol increases to Rs. 8 per km. He has Rs. 600 to spend on petrol and wishes to travel the maximum distance within an hour. Formulate the above problem as LPP.
Answers
Let John travel x1 km at a speed of 60 km/hour and x 2km at a speed of 90 km/hour.
Therefore, time required to travel a distance of x 1
km is 60x 1 hours and the time required to travell a distance of x 2 km is 90x 2 hours.
∴ total time required to travel is ( 60x 1+ 90x 2 )hours.
Since he wishes to travel the maximum distance within an hour.
( 60x 1 + 90x 2)≤1
He has to spend □ 5per km on petrol at a speed of 60 km/hour and □8 per km at a speed of 90 km/hour
∴ the total coist of travelling is □(5x 1+8x 2 )
Since he has □ 600 to spend on petrol,
5x 1 +8x 2 =≤600
Since distance is never negative,x1≥0,x 2 ≥0.
Total distance traveled by John is z = (x 1+x 2 ) km.
This is the linear function which is to be maximized.
Hence, it is objective function.
Hence, the given LPP can be formulated as:
Maximize z = x 1 +x 2 , subject to
( 60x + 90x 2 )≤1,5x 1+8x 2=≤600,x1≥0,x 2≥0