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Q60Section B (Part B)60 of 120

Maximise x+yx+y over a polygon

Solve the following linear programming problem:

maximize z=x+yz=x+y subject to

5x+3y≤30,2x+6y≤25,2x−y≤8,x≥0,y≥0.5x+3y\le30,\qquad 2x+6y\le25,\qquad 2x-y\le8,\qquad x\ge0, y\ge0.

Then the optimal value of the objective function is

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