Answer:
The point that maximizes the objective function is (3,0)
Step-by-step explanation:
we have
Constraints:
[tex]x\geq 0\\y\geq 0\\-x + 3\geq y\\y\leq \frac{1}{3}x+1[/tex]
Using a graphing tool
The feasible region is the shaded area
see the attached figure
The vertices of the feasible region are
(0,0),(0,1),(1.5,1.5) and (3,0)
we know that
To find the point in the feasible region that maximizes the objective function, replace each ordered pair of vertices in the objective function and then compare the results.
The objective function is
[tex]C=5x-4y[/tex]
For (0,0) -----> [tex]C=5(0)-4(0)=0[/tex]
For (0,1) -----> [tex]C=5(0)-4(1)=-4[/tex]
For (1.5,1.5) -----> [tex]C=5(1.5)-4(1.5)=1.5[/tex]
For (3,0) -----> [tex]C=5(3)-4(0)=15[/tex]
therefore
The point that maximizes the objective function is (3,0)
