Refer to question 15. Determine the maximum distance that the man can travel.
Referring to solution 15, we have
Maximise Z =x+y, subject to
2x+3y≤120,8x+5y≤400,x≥0,y≥0
On solving, we get
8x+5y =400 and 2x+3y =120, we get
x=3007,y=807
From the shaded feasible region, it is clear that coordinates of corner points are (0,0).(50,0), (3007,807) and (0,40).
Corner pointsCorresponding value of Z=x+y(0,0)0(50,0)503007,8073807=5427km←Maximum(0,40)40
Hence, the maximum distance that the man can travel is 54 27km.