Answer:
The minimum value of C is 14
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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