Find the maximum value of p= 4x + 5y subject to the following constraints :

 The maximum value of P is 38 at (7,2)

Step-by-step explanation:

To find the maximum value of

Subject to the following constraints:-

From this we get boundary equations of the given inequalities as

Now, find points from which the above lines are passing.

In (1) at y=0, x=13

At y=1, x=10

So line (1) passing through (13,0) and (10,1)

Similarly, In (2), at x=1, y=11

At y=2, x=7

So line (2) is passing through (1,11) and (7,2)

Plot theses lines on the graph by using these points .

Corner points of the shaded region = (0,4.33) , (8,33,0) and (7,2)

The  value of P at corner points :-

Clearly, the maximum value of P is 38 at (7,2)

thats not a system of equations, that is a solution