10. The optimal solution of a maximization type LPP is given in the following table:
C sj
′ 6 4 0 0 0
Solution
CB
Basic Variables
1
x 2
x 3
x 4
x 5
x
0 3
x 0 5/3 1 − 3/2 0 14
0 5
x 0 − 3/1 0 1/3 1 5
6 1
x 1 2/3 0 1/3 0 8
Cj − Z j
0 0 0 − 2 0 Z = 48
(i) Find the alternative optimal basic feasible solution.
(ii) Find an alternative optimal non-basic feasible solution.
(i) "2x_1 + x_2 \u22641000\\\\\n\nx_1 + x_2 \u2264 800\\\\x_1,x_2\\ge0"
"Z=4x_1+3x_2"
The graphical region of the given inequalities is-
The critical points are-
(200,600) "Z=4x_1+3x_2=4(200)+3(600)=800+1800=2600"
(500,0) "Z=4x_1+3x_2=4(500)+3(0)=2000+0=2000"
(0,800) "Z=4x_1+3x_2=4(200)+3(600)=0+2400=2400"
(0,0) "Z=4x_1+3x_2=4(0)+3(0)=0+0=0"
The maximum value of Z is 2600 at "x_1=200,x_2=600"
(ii) As calculating above,
The alternative non feasible solution is "x_1=500,y_1=0"
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