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Find graphically the solution sets of each of the following systems of inequalities :
`3x_(1) + x_(2) le 66`
`x_(1) + x_(2) le 45`
`x_(1) le 20`
`x_(2)le 40`
and `x_(1), x_(2) ge 10`

Answer

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Knowledge Check

  • By graphical method, the solutions of linear programming problem maximise Z=3x_(1)+5x_(2) subject to constraints 3x_(1)+2x_(2) le 18, x_(1) le 4, x_(2) le 6 x_(1) ge0,x_(2) ge 0 are

    A
    `x_(1)=2,x_(2)=0,Z=6`
    B
    `x_(1)=2,x_(2)=6,Z=36`
    C
    `x_(1)=4,x_(2)=3,Z=27`
    D
    `x_(1)=4,x_(2)=6,Z=42`

  • The LPP problem Max z=x_(1)+x_(2) such that -2x_(1)+x_(2)le1,x_(1)le2,x_(1)+x_(2)le3 and x_(1),x_(2)ge0 has

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    One solution
    B
    Three solutions
    C
    Infinite number of solutions
    D
    No solution

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