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Question

Solve the following linear programming problem graphically:

Maximise Z=34x+45y

under the following constraints

x+y3002x+3y70x,y0


Solution



Here, objective function of given LPP is:

Maximise Z=34x+45y

Subject to the constraints:

x+y3002x+3y70x,y0

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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