Problem 2 (a) Convert the following LP with the two decision variables 21, 22 ma

Question

Problem 2 (a) Convert the following LP with the two decision variables 21, 22 maximize subject to 2z1 + 22 21 2 z2 t22 3 to the vector notation form subject to Ar2b 20 Clearly indicate what x, c, A, and b are. If you have added or replaced any decision variables, clearly indicate the relationship between the original decision variables and the new ones. Also, clearly indicate the relationship between the value of your new objective function and the original one (b) Show how r - 1/2| S 1/2 can be represented in terms of linear constraints. (c) If Ix -1/2l 2 1/2 could be represented in terms of linear constraints, then we could represent binary variables (variables that can only take values in the set 0,1 n LPs. In one concise sentence, explain why this is true (d) Can |u - 1/2l 2 1/2 be represented in terms of linear constraints? Explain your answer in one concise sentence.

Explanation / Answer

Z = 2z1 +z2

z1 > = z2

z1 - z2 >= 0

z1+z2 < = 3

-z1 -z2 >= -3

x = [z1 ; z2]   {column vector}

c = [ 2 ;1];

A =[ 1 -1 ; -1 -1];

b =[0 ; -3];

c =

     2
     1

>> A

A =

     1    -1
    -1    -1

b =

     0
    -3

b)

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