A man rides his motorcycle to the speed 50 km/h. He has to spend 2per km on petrol. If the rides it at a faster speed of 80km/h, the petrol cost increases to 3 per km. He wishes to find the maximum distnace that he can travel. Express this problem as a linear programming problem.
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Let the man rides to his motorcycles to a distance x km at the speed of 50km/h and also distance y km at the speed of 80km/h. Therefore cost on petrol is 2x+3y. Since, he has to spend 120 on petrol. `2x+3yle 120` Also ,he has atmost one hour time. `(x)/(50)+(y)/(80)le 1` `Rightarrow 8x+5y le 400` Also, we have ` x le 0, y le 0` [ non negative constraints] Thus, required LPP to travel maximum distance by him is Maximise Z=x+y, Subjected to `2x+3y le 120, 8x+5y le 400, x ge 0, y ge 0`
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