Consider the following problem. Maximize Z = c1x1 + c2x2, Subject to and x1

Consider the following problem.
Maximize Z = c1x1 + c2x2,
Subject to
Consider the following problem.
Maximize Z = c1x1 + c2x2,
Subject to
and
x1

and
x1 ≥ 0, x2 ≥ 0.
Let x3 and x4 denote the slack variables for the respective functional constraints. When c1 = 3, c2 = –2, b1 = 30, and b2 = 10,

Consider the following problem.
Maximize Z = c1x1 + c2x2,
Subject to
and
x1

the simplex method yields the following final simplex tableau.
I (a) Use graphical analysis to determine the allowable range for c1 and c2.
(b) Use algebraic analysis to derive and verify your answers in part (a).
I (c) Use graphical analysis to determine the allowable range for b1 and b2.
(d) Use algebraic analysis to derive and verify your answers in part (c)
C (e) Use a software package based on the simplex method to find these allowable ranges.

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