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Question

Solve the following linear programming problem graphically.
Minimize Z = 3x+5y

Subject to the constraints x+2y10,x+y6,3x+y8,x0,y0. Tominimize:z=3x+5ySubjecttotheconstraintsx+2y10,x+y6,3x+y8,x0,y0

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Solution


Critical PointsValue of zA(10,0)30B(2,4)26Min. ValueC(1,5)28D(0,8)40

As the feasible region is unbounded; therefore 26 may or may not be the minimum value of z. In order to check, we plot the graph of inequality 3x+5y <26.

It can be seen easily that the feasible region has no common point with 3x+5y< 26 therefore, the minimum value of z is 26.


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