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Question
Solve the following problem:
Maximize Z=−Px1+4x2
Subject to: −3x1+x2≤6
x1+2x2≤4
x2≤−3
No lower bound constraint for x1
Maximize Z=−Px1+4x2
Subject to: −3x1+x2≤6
x1+2x2≤4
x2≤−3
No lower bound constraint for x1
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Solution
The third constraint can be re-written as −x2≥3. The solution space satisfying constraints is shown shaded in the figure.
A(−3,−3) and B(10,−3) value of the objective functions Z=−x1+4x2 at these vertices are
Z(A)=3−12=−9, Z(B)=−10−12=−22
Thus the maximum value of Z occurs at A. Hence the solution to the problem is
x1=−2,x2−3;Zmax=−9
A(−3,−3) and B(10,−3) value of the objective functions Z=−x1+4x2 at these vertices are
Z(A)=3−12=−9, Z(B)=−10−12=−22
Thus the maximum value of Z occurs at A. Hence the solution to the problem is
x1=−2,x2−3;Zmax=−9
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