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minimum and maximum values of the objective function

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Sketch the region determined by the given constraints. Then find the minimum and maximum values of the objective function and where they occur, subject to the given constraints. Constraints: y<= -3x+6, y <= -x+3, y>=0, x>=0 and the objective function is z=2x-3y.

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Determine the minimum and maximum values of the objective function.

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Please see attached for sketch.

Constraints: y<= -3x+6, y <= -x+3, y>=0, x>=0 and the objective function is z=2x-3y
Plotting the line y=-3x+6 on the plane, we see that the x and y intercepts are (2, 0) and (0, 6) respectively.
Plotting the line ...

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