Answer:
The value that maximize the objective function is the point (1,4)
Step-by-step explanation:
we have
[tex]3x+y\leq 7[/tex] ----> inequality A
[tex]x+2y\leq 9[/tex] ----> inequality B
[tex]x\geq 0[/tex] ----> inequality C
[tex]y\geq 0[/tex] ----> inequality D
Using a graphing tool
The solution is the shaded area
see the attached figure
The coordinates of the solution area are
[tex](0,0),(0,4.5),(1,4),(2.33,0)[/tex]
we have
The Objective Function is equal to
[tex]P=2x+y[/tex]
To find out the value of x and y that maximize the objective function, substitute each ordered pair of the vertices in the objective function and then compare the results
For (0,0) --------> [tex]P=2(0)+0=0[/tex]
For (0,4.5) --------> [tex]P=2(0)+4.5=4.5[/tex]
For (1,4) --------> [tex]P=2(1)+4=6[/tex]
For (2.33,0) --------> [tex]P=2(2.33)+0=4.66[/tex]
The value that maximize the objective function is the point (1,4)
