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.
The figure below shows the plan of a town. A person "X" rides his bicycle from house at A to office at B, taking the shortest route. The number of shortest paths that he can choose is: