Answer: The maximum value: P = 6x + 7y - 2 is 84 at (5,8).
Explanation:
Here, Object of constraint P(max) = 6x + 7y - 2.
And, the system of constraints,
x≤5, y≤(1/5)x + 7, x≥0, y≥0
Since, x= 5 is a line parallel to y-axis.
And at origin it is giving 0≤5 ( false)
Thus the area of inequality x≤5 does not contain the origin.
Now, x -intercept and y-intercept of line y=(1/5)x + 7 are (-35,0) and (0, 7) respectively.
Also, at (0, 0), 0 ≤(1/5)×0 + 7 (true)
Therefore, inequality y≤(1/5)x + 7 will contain the origin.
Now, x≥0, y≥0 shows the first quadrant.
Thus, we get feasible region ABCD.
In which at A≡(0,7), P = 49.
At B≡(5,8), P= 84,
At C≡(5,0), P= 30,
And, D≡(0,0), P= 0
Therefore at B, P is maximum.