Answer:
The maximum value of C is 14
Step-by-step explanation:
we have the following constraints
[tex]x\geq 0[/tex] ----> constraint A
[tex]y\geq 0[/tex] ---> constraint B
[tex]2x+2y\leq 10[/tex] ---> constraint C
[tex]3x+y\leq 9[/tex] ---> constraint D
Determine the area of the feasible region using a graphing tool
see the attached figure
The vertices of the feasible region are
[tex](0,0),(0,5),(2,3),(3,0)[/tex]
To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertices in the objective function an then compare the results
we have
[tex]C=4x+2y[/tex]
For (0,0) ----> [tex]C=4(0)+2(0)=0[/tex]
For (0,5) ----> [tex]C=4(0)+2(5)=10[/tex]
For (2,3) ----> [tex]C=4(2)+2(3)=14[/tex]
For (3,0) ----> [tex]C=4(3)+2(0)=12[/tex]
therefore
The maximum value of C is 14
