Here, we are required to find the values of x and y that maximize the objective function; N=100x+40y given the constraint equations as in the question.
The values of x and y that maximixe the objective function are 8 and 0 respectively. i.e (8,0)
The coordinates of points( vertexes ) in the graph must first be determined.
Therefore, for equation x+y≤8
- The coordinates are (8,0) and (0,8)
Therefore, for equation 2x+y≤10
- The coordinates are (5,0) and (0,10)
However, at the point of intersection of the two aforementioned constraint equations, the coordinate can be gotten by solving simultaneously; to yield;
- The coordinates of the point of intersection are : (2,6)
Therefore, by testing the objective function with all of the x and y values as follows;
- For (8,0), we have; N=100(8)+40(0), N=800
- For (0,8), we have; N=100(0)+40(8), N=320
- For (5,0), we have; N=100(5)+40(0), N=500
- For (0,10), we have; N=100(0)+40(10), N=400
- For (2,6), we have; N=100(2)+40(6), N=440
Therefore, the values of x and y that maximixe the objective function are 8 and 0 respectively.
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