Let the man rides his motorcycle for a distance of x km at a speed of 50km/hr then he has to spend Rs. 2/km on petrol.

let the man rides his motorcycle for a distance of y km at a speed of 80 km/hr then he has to spend Rs. 3/km on petrol.

He has at most Rs 120 to spend on petrol for total distance covered so the constraint becomes,

2x+3y≤120…………(i)

Now also given he has at most one hour’s time for total distance to be covered, so the constraint becomes

{as distance=speed×time}

Now taking the LCM as 400, we get

⇒ 8x+5y≤400……………(ii)

And x≥0, y≥0 [non-negative constraint]

He want to find out the maximum distance travelled, here total distance, Z =x+y

Now, we have to maximize the distance, i.e., maximize Z=x+y

So, to maximize distance we have to maximize, Z=x+y, subject to

2x+3y≤120

8x+5y≤400

x≥0, y≥0