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

The minimum value of C is 14

Step-by-step explanation:

Sketch the graph of the constraints using

2x + y = 20

with intercepts (0, 20) and (10, 0)

2x + 3y = 36

with intercepts (0, 12) and (18, 0)

The solution to both are above the lines

Solve 2x + y = 20 and 2x + 3y = 36 to find the point of intersection at (6, 8)

Then the coordinates of the vertices of the region formed are

(0, 20), (6, 8) and (18, 0)

Evaluate the objective function at each vertex to determine minimum value

C = 0 + 20 = 20

C = 6 + 8 = 14

C = 18 + 0 = 18

Thus the minimum value of C is 14 when x = 6 and y = 8

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