A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has at most Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.
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Answer: 54.3 km
Step-by-step explanation:
let x and y be the distances travelled by man in 50 km/hr and 80 km/hr respectively.
distance to be travelled in rs 120,
120 > 2x+3y
Maximum time,
1 > x/50+y/80
Maximum distance he can travel = x+y
x y distance
0 40 40
300/7 80/7 380/7 = 54.3
50 0 50
from the above values, the maximum distance that can be covered in 1 hr and rs 120 is 54.3 km.
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