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Answer:
C = 6 is the minimum
Step-by-step explanation:
2-variable constraint problems are often easy to solve graphically. The overlap of each of the solution regions defines a "feasible region." The vertices of that region will be candidates for the (x, y) values that satisfy the objective function.
The three constraints define a feasible region with four vertices:
The most likely candidates for minimizing C are (0, 2) and (3, 0). The corresponding values of C are ...
(0, 2): C = 4·0 +3·2 = 6
(3, 0): C = 4·3 +3·0 = 12
The minimum value of C is 6 at (x, y) = (0, 2).
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Additional comment
The line representing the objective function will be closest to the origin when the objective function is minimized. Once we can see the slope of it on the graph, we can determine the feasible region boundary point that will place the line closest to the origin.
