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Question
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 atmost 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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Solution
Let the man covers x km on his motorcycle at the speed of 50 km/hr and covers y km at the speed of 80 km/hr.
So, cost of petrol = 2x + 3y
The man has to spend ₹ 120 atmost on petrol
∴ 2x + 3y ≤ 120 ......(i)
Now, the man has only 1 hr time
∴ `x/50 + y/80 ≤ 1`
⇒ 8x + 5y ≤ 400 .....(ii)
x ≥ 0, y ≥ 0
To have maximum distance Z = x + y.
Hence, the required LPP to travel maximum distance is maximise Z = x + y
Subject to the constraints 2x + 3y ≤ 120, 8x + 5y ≤ 400, x ≥ 0, y ≥ 0.
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