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Rewrite the System of Inequalities, Adding Slack Variables or Subtracting x1+x2+x341\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3} \leq 41

Question 156

Multiple Choice

Rewrite the system of inequalities, adding slack variables or subtracting surplus variables as needed.
- x1+x2+x341\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3} \leq 41
x1+x2+x323x_{1}+x_{2}+x_{3} \geq 23
x1+x214\mathrm{x}_{1}+\mathrm{x}_{2} \geq 14


A) x1+x2+x3s1=41x_{1}+x_{2}+x_{3}-s_{1}=41
x1+x2+x3s2=23\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}-\mathrm{s}_{2}=23
x1+x2s3=14\mathrm{x}_{1}+\mathrm{x}_{2}-\mathrm{s}_{3}=14
B) x1+x2+x3+s1=41x_{1}+x_{2}+x_{3}+s_{1}=41
x1+x2+x3+s2=23\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{s}_{2}=23
x1+x2+s3=14\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{s}_{3}=14
C) x1+x2+x3s1=41x_{1}+x_{2}+x_{3}-s_{1}=41
x1+x2+x3+s2=23\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{s}_{2}=23
x1+x2+s3=14\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{s}_{3}=14
D) x1+x2+x3+s1=41\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{s}_{1}=41
x1+x2+x3s2=23\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}-\mathrm{s}_{2}=23
x1+x2s3=14\mathrm{x}_{1}+\mathrm{x}_{2}-\mathrm{s}_{3}=14

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