For the following linear programming problem
Max Z 0.5x1 + 6x2 + 5x3
s.t. 4x1 + 6x2 + 3x3 ? 24
1x1 + 1.5x2 + 3x3 ? 12
3x1 + x2 ? 12
a. Find the range of optimality for c1, c2, c3, c4, c5, and c6.
b. Find the range of feasibility for b1, b2, and b3.
a. c1 ? 4
2.5 < c2 ? 10
3 < c3 ? 12
c4 ? 0.77
c5 ? 0.88
?1.5 ? c6 ? 3.5
b. 12 ? b1 ? 48
6 ? b2 ? 24
b3 ? 2.67
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