!graph the system of constraints: x≤5, y≤(1/5)x + 7, x≥0, y≥0. find all vertices. evaluate the objective function at each vertex to find the maximum value: p = 6x + 7y - 2.

The maximum value: P = 6x + 7y - 2 is 84 at (5,8).

Step-by-step 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.