Question

Solve the following linear programming problem graphically: Maximise Z=34x+45y under the following constraints x+y≤3002x+3y≤70x≥,y≥0

Solution

Here, objective function of given LPP is: Maximise Z=34x+45y Subject to the constraints: x+y≤3002x+3y≤70x≥,y≥0 Consider x+y=300 Table of solutions is: x3000y0300 Consider 2x+3y=70 Table of solutions is: x352y022 To solve the LPP, we draw the graph of the inequations and get the feasible solution shown (shaded) in the graph,. Corner points of the common shaded region are P(0,0), A(35,0) and B(0,703). Value of Z at each corner point is given as Corner PointsValue of the objective function                 Z=34x+45yAt O(0,0)Z=0+0=0At A(35,0)Z=34×35+0=1190At B(0,703)Z=0+45×703=1050 Hence, maximum value of Z is 1190 and it is obtained when x=35 and y=0

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