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in Mathematics by (54.1k points)

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.

1 Answer

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by (88.2k points)
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Best answer

Let the man rides to his motorcycle to a distance x km at the speed of 50 km/h and to a distance y km at the speed of 80 km/h.

Therefore, cost on petrol is 2x + 3y.

Since, he has to spend Rs120 atmost on petrol.

∴ 2x + 3y ≤ 120 …(i)

Also, he has at most one hour’s time.

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