Question

1 The LP problem in this case is: Maximize z = 6x? + 2x? + 12x? subject to 4x? + x? + 3x? ? 24 2x? + 6x? + 3x? ? 30 x? ? 0, x? ? 0, x? ? 0 The final tableau is given: z x? x? x? s? s? RHS BV 1 10 2 0 4 0 96 z 0 4/3 1/3 1 1/3 0 8 x? 0 -2 5 0 -1 1 6 s? (a) Write down the solution to the maximizing problem (b) Write down the dual of the given maximizing problem (c) Write down the solution of the dual minimizing problem (d) In the notation from class, what is the matrix B?¹ for this optimal tableau? (e) Suppose that 24 and 30 on the RHS of the constraints were replaced by new values b? and b? respectively. Find conditions on b? and b? to keep the current set of basic variables the same. (f) Use your answer from Part (e) to find individual ranges for b? and b? (g) In the notation from class, what is c??? for this problem? (h) Find the range for c? to keep the original set of x-values optimal.

          1 The LP problem in this case is:
Maximize z = 6x? + 2x? + 12x? subject to 4x? + x? + 3x? ? 24
2x? + 6x? + 3x? ? 30
x? ? 0, x? ? 0, x? ? 0
The final tableau is given:
z x? x? x? s? s? RHS BV
1 10 2 0 4 0 96 z
0 4/3 1/3 1 1/3 0 8 x?
0 -2 5 0 -1 1 6 s?
(a) Write down the solution to the maximizing problem
(b) Write down the dual of the given maximizing problem
(c) Write down the solution of the dual minimizing problem
(d) In the notation from class, what is the matrix B?¹ for this optimal tableau?
(e) Suppose that 24 and 30 on the RHS of the constraints were replaced by new values b? and b? respectively. Find conditions on b? and b? to keep the current set of basic variables the same.
(f) Use your answer from Part (e) to find individual ranges for b? and b?
(g) In the notation from class, what is c??? for this problem?
(h) Find the range for c? to keep the original set of x-values optimal.

1 The LP problem in this case is:
Maximize z = 6x? + 2x? + 12x? subject to 4x? + x? + 3x? ? 24
2x? + 6x? + 3x? ? 30
x? ? 0, x? ? 0, x? ? 0
The final tableau is given:
z x? x? x? s? s? RHS BV
1 10 2 0 4 0 96 z
0 4/3 1/3 1 1/3 0 8 x?
0 -2 5 0 -1 1 6 s?
(a) Write down the solution to the maximizing problem
(b) Write down the dual of the given maximizing problem
(c) Write down the solution of the dual minimizing problem
(d) In the notation from class, what is the matrix B?¹ for this optimal tableau?
(e) Suppose that 24 and 30 on the RHS of the constraints were replaced by new values b? and b? respectively. Find conditions on b? and b? to keep the current set of basic variables the same.
(f) Use your answer from Part (e) to find individual ranges for b? and b?
(g) In the notation from class, what is c??? for this problem?
(h) Find the range for c? to keep the original set of x-values optimal.

Added by Carrie J.

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