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
Solve the system of inequalities by graphing
using a graphing tool
The solution is the quadrilateral shaded area
see the attached figure
The vertex of the figure are
(0,0),(0,5),(2,3) and (3,0)
To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertex in the objective function C and then compare the results
we have
[tex]C=4x+2y[/tex]
[tex]For (0,0) -----> C=4(0)+2(0)=0\\For (0,5) -----> C=4(0)+2(5)=10\\For (2,3) -----> C=4(2)+2(3)=14\\For (3,0) -----> C=4(3)+2(0)=12[/tex]
therefore
The maximum value of C is 14
