Question

Algebra Consider the feasible region in R3 defined by the inequalities -X1 + X3 > 4 3x1 + 2x2 – 23 > -3, along with xi > 0, x2 > 0 and x3 > 0. (a) Write down the linear system obtained by introducing slack vari- ables 24 and 25. (b) Write down the basic solution corresponding to the variables xi and X3. (c) Explain whether the solution corresponds to a vertex of the fea- sible region. If it does then find the vertex.

Answer 1

# a. solution: We are given feasible region in R3 (a) Want to write linear system, introducing slack variables Zaand as. We are given inequalities, - 4+X, > 4 2 [ -(U 3x + 2x₂ - X₂ 7-3 I shus, stack variables xa and to, above inequalities becomes - x + 2 + x4 = 4. 3x + 2x₂ - X₂ + x = – 7 4 X₂, X₂, XA, Xs > 0 (6) want to find basic solution. To variables x and az So, for basic solution R2, X, as must be equal zero. i..., x.= 0 = x= x5 hame, egh in (a) becomes –4 +23=4 & 34 -&z= - 3 on solung, we get r 1204 + + + 2 = Ye * x3 = 4+1/2 - 9/. (c) solution (1,0,0,0,0), satisfy inequalities in car (W. The solution corresponds as 30, 200) as this & a basis feasible solution.

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