Answer:
The minimum value of C is 20
Step-by-step explanation:
we have
[tex]2x+3y\geq 24[/tex] ----> constraint A
[tex]4x+y\geq 38[/tex] ----> constraint B
[tex]x\geq 0[/tex] ----> constraint C
[tex]y\geq 0[/tex] ----> constraint D
Using a graphing tool
The solution set of the constraints is the shaded area
see the attached figure
The vertices of the shaded area are (0,38),(9,2) and (12,0)
To determine the minimum value of C substitute the values of x and y of each vertex in the objective function and then compare the results
[tex]C=2x+y[/tex]
For (0,38) ---> [tex]C=2(0)+38=38[/tex]
For (9,2) ---> [tex]C=2(9)+2=20[/tex]
For (12,0) ---> [tex]C=2(12)+0=24[/tex]
therefore
The minimum value of C is 20
