Q. 155.0( 2 Votes )

A man rides his m

Answer :

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


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