Answer:
The maximum value of P=11 occurs at x=1 and y=4
Step-by-step explanation:
we have
[tex]y\leq -2x+6[/tex] ----> constraint A
[tex]y\leq x+3[/tex] ----> constraint B
[tex]x\geq 0[/tex] ----> constraint C
[tex]y\geq 0[/tex] ----> constraint D
using a graphing tool
The solution is the shaded area
see the attached figure
The vertices of the solution area are
(0,0),(0,3),(1,4),(3,0)
Substitute the value of x and the value of y of each vertex in the objective function , to find out the maximum value of P
The objective function is
[tex]P=-x+3y[/tex]
For (0,0) -----> [tex]P=-(0)+3(0)=0[/tex]
For (0,3) -----> [tex]P=-(0)+3(3)=9[/tex]
For (1,4) -----> [tex]P=-(1)+3(4)=11[/tex]
For (3,0) -----> [tex]P=-(3)+3(0)=-3[/tex]
therefore
The maximum value of P=11 occurs at x=1 and y=4
