Find the minimum value of c=2x+3y subject to the following constraints

 19

Step-by-step explanation:

Step 1 - find the vertices

You can do this by solving the systems of equations to find the coordinate where each pair of equations intersect ..or.. by graphing.

I chose to graph it - (see attachment)- purple is the intersection

Vertices are: (0, 29/3), (5,3), & (11, 0)

Step 2 - find the minimum

Plug all of the vertex coordinates into the given equation and look for the lowest value.

C = 2x + 3y

(0, 29/3): 2(0) + 3(29/3)   =    0 + 29    = 29

(5, 3):      2(5)  +    3(3)      =  10  +  9     = 19   → this is the minimum!

(11, 0):      2(11)  +   3(0)      =  22  + 0     = 22