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,
Now also given he has at most one hour’s time for total distance to be covered, so the constraint becomes
Now taking the LCM as 400, we get
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
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