Solve the following linear programming problem graphically:
Maximise Z=34x+45y
under the following constraints
x+y≤3002x+3y≤70x≥,y≥0
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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)andB(0,703).
Value of Z at each corner point is given as Corner PointsValue of the objective functionZ=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