Answer:
The minimum value of C is 20
Step-by-step explanation:
we have
[tex]2x+3y\geq 24[/tex] ----> constraint 1
[tex]4x+y\geq 38[/tex] ----> constraint 2
[tex]x\geq 0[/tex] ----> constraint 3
[tex]y\geq 0[/tex] ----> constraint 4
using a graphing tool
The solution is the shaded area
see the attached figure
To find the minimum value of C evaluate the vertices (9,2) and (12,0) of the solution area in the objective function [tex]C=2x+y[/tex]
so
For x=9, y=2 ---> [tex]C=2(9)+2=20[/tex]
For x=12, y=0 ---> [tex]C=2(12)+0=24[/tex]
therefore
The minimum value of C is 20
