Unformatted text preview: 1. Convert the following linear programming problem to standard form and
then write out the coefﬁcient matrix A. Maximize 33:1 — x2 + 4
subject to IV
._\ $1 — $2
—2IE1 + 3:172
901 S 2, 902 free 2. Consider the linear programming problem below (in standard form). (a)
Write the basic feasible solution corresponding to the basis {$2,533}. (b)
Perform the Optimality Test of the Simplex Method to determine whether the basis {$2,353} is optimal.
Minimize z = —3x1 —— 5392 + x3 subject to 4171 + 3.112 + $4 = 2
—2$2 + $3 + $5 $171,332, $3,x4,$5 Z 0 
._.. 3. Consider the primal linear programming problem in canonical form below.
(a) Show that x = (1,1,1,2)T is a feasible solution to the problem. (b) Label
each of the constraints of the problem as active or inactive for the feasible
solution a: = (1,1,1,2)T. (0) Determine all values of a such that the vector
p = (—1,1,1,a)T is a feasible direction at the feasible solution x = (1, 1, 1, 2).
(d) Write the objective function of the dual linear programming problem, but
no other part of that problem. (Note that part ((1) has nothing to do with
any other part of this question.) ...
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 Spring '10
 Brown

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