Consider a challenge in capital budgeting where six projects are represented by0−1variablesx1,x2,x3,x4,x5,andx6.a. Write a constraint...

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Consider a capital budgeting problem with 6 projects represented by 0 or 1 and variables ${\displaystyle x_1,x_2,x_3,x_4,x_5,x_6.}$
For part (a) it is required to find the constraint modelling a situation in which two of the project 1,3 and 6 must be undertaken.
${\displaystyle x_1+x_3+x_6\ge 2}$ For part (b) it is required to find the situation of the constraint ${\displaystyle x_3-x_5=0.}$
constraint: ${\displaystyle x_3-x_5=0}$
Project 3 and 5 must be selected together and none of them cannot be selected alone
${\displaystyle \text{so}<(x_3,x_5)=(1,1)\text{or}(0,0)}$
${\displaystyle \Rightarrow x_3-x_5=0}$
For part (c) it is required to write a constraint modelling a situation in which project 2 or 4 must be taken but not both.
${\displaystyle x_2+x_4=1}$
From the above constraint it is assure that one of the project is taken at a time not both as either
$0+1=1\text{or}1+0=1$