Answer: The maximum value of P is 38 at (7,2)
Step-by-step explanation:
To find the maximum value of [tex]P=4x+5y[/tex]
Subject to the following constraints:-
[tex]x+3y\leq13\\3x+2y\leq25\\x\leq0,y\leq0[/tex]
From this we get boundary equations of the given inequalities as
[tex]x+3y=13...........(1)\\3x+2y=25....................(2)\\x=0,y=0[/tex]
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 :-
[tex]\P=4(0)+5(4.33)=21.65\P=4(8.33)+0=33.32\\P=4(7)+5(2)=38[/tex]
Clearly, the maximum value of P is 38 at (7,2)
