Answer:
The maximum value of C is 15
Step-by-step explanation:
we have
[tex]x\geq 0[/tex] -----> constraint A
[tex]y\geq 0[/tex] -----> constraint B
[tex]2x+y\leq 10[/tex] -----> constraint C
[tex]3x+2y\leq 18[/tex] -----> constraint D
using a graphing tool
The solution area of the constraints in the attached figure
we have the vertices
(0,0),(0,9),(2,6),(5,0)
Substitute the value of x and the value of y in the objective function
(0,0) -----> [tex]C=3(0)-2(0)=0[/tex]
(0,9) -----> [tex]C=3(0)-2(9)=-18[/tex]
(2,6) -----> [tex]C=3(2)-2(6)=-6[/tex]
(5,0) -----> [tex]C=3(5)-2(0)=15[/tex]
therefore
The maximum value of C is 15
