assign4_5 - α β γ δ and ε in the tableau are unknown...

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CO 350 Assignment 4.5 – Winter 2010 Not to be handed in 1. Consider the LP problem maximize c T x subject to Ax = b, x 0, where c = - 1 1 - 1 - 1 - 1 1 , A = 1 0 0 1 0 6 3 1 - 4 0 0 2 1 0 2 0 1 2 , and b = 9 2 6 . (a) Find the tableau corresponding to the basis { 1 , 2 , 3 } and to the basis { 1 , 4 , 5 } . Which of them is feasible? (b) Beginning with a feasible tableau from part (a), solve the problem with the simplex method. 2. Consider the linear programming problem ( P ) max { c T x : Ax b, x 0 } , where A = 2 1 - 1 - 1 - 1 1 0 3 1 - 1 1 - 1 , b = 3 1 1 , c = 1 0 1 - 1 . (a) Put the problem into standard equality form, and, beginning with all slack variables basic, solve with the simplex method, using the smallest subscript rule for choosing the entering variable. (b) Is the optimal solution you found in part (a) the only optimal solution? Explain. 3. The following is a tableau of a maximization problem, where the entries
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Unformatted text preview: α , β , γ , δ and ε in the tableau are unknown parameters. z + δx 4 + γx 5 = x 2 + αx 4 = 3 x 3-2 x 4 + εx 5 = 2 x 1 + 2 x 5 = β For each of the following statements, ±nd conditions on the values of α , β , γ , δ and ε such that the statement is true. (a) The basic solution is not feasible. (b) The basic solution is feasible, but the tableau is not optimal. (c) The basic solution is feasible, x 5 is a candidate for entering the basis, and when x 5 enters the basis, then x 3 must leave the basis. (d) The basic solution is feasible and the next iteration, under the smallest subscript rule (see Section 6.6), indicates that the problem is unbounded. 1...
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