Answer:
The minimum value of C is 6, for x=0 and y=2
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+3y\geq 6[/tex] ---> constraint C
[tex]3x-2y \leq 9[/tex] ---> constraint D
[tex]x+5y\leq 20[/tex] ---> constraint E
using a graphing tool
Find out the feasible region
The feasible region is the shaded area
see the attached figure
The vertex of the feasible region are
(0,2),(0,4),(5,3) and (3,0)
The objective function is
[tex]C=4x+3y[/tex]
To find out the minimum value, substitute the value of x and the value of y of each vertices in the objective function and then compare the results
For (0,2) --->[tex]C=4(0)+3(2)=6[/tex]
For (0,4) --->[tex]C=4(0)+3(4)=12[/tex]
For (5,3) --->[tex]C=4(5)+3(3)=29[/tex]
For (3,0) --->[tex]C=4(3)+3(0)=12[/tex]
therefore
The minimum value of C is 6, for x=0 and y=2
