# Question

Consider the following problem.

Maximize Z = c1x1 + c2x2,

Subject to

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,

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.

Maximize Z = c1x1 + c2x2,

Subject to

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,

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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