Question

A man rides his motorcyle at the speed of 50 km/h. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/h, the petorl 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.

Answer 1

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 Rs 120 atmost on petrol.
$\therefore 2x+3y\le \mathrm{120.......}\left(i\right)$
Also, he has atmost one hour's time.
$\therefore \frac{x}{50}+\frac{y}{80}\le 1\Rightarrow 8x+5y\le \mathrm{400......}\left(ii\right)$
Also, we have $x\ge 0,y\ge 0$ [non-negative constraints]
Thus, required LPP to travel maximum distance by him is Maximise Z =x+y, subject to $2x+3y\le 120,8x+5y\le 400,x\ge 0,y\ge 0$