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STD 12 - 12. linear programming — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 12. linear programming1 Mark
MCQ
The solution of linear programming problem, maximize $\mathrm{Z}=3 x_{1}+5 x_{2}$ subject to $3 x_{1}+$ $2 x_{2} \leq 18, x_{1} \leq 4, x_{2} \leq 6, x_{1} \geq 0, x_{2} \geq 0$ is $.....$
  • A
    $x_{1}=2, x_{2}=0, z=6$
  • ✓
    $x_{1}=2, x_{2}=6, z=36$
  • C
    $x_{1}=4, x_{2}=3, z=27$
  • D
    $x_{1}=4, x_{2}=6, z=42$
✓

Answer

Correct option: B.
$x_{1}=2, x_{2}=6, z=36$
b
$x_{1}=2, x_{2}=6, z=36$

If we take the maximum value of $\mathrm{Z}$ as $42, x_{1}=4, x_{2}=6$

$\therefore 3 x_{1}+2 x_{2}=24 \leq 18$ which is not true.

$x_{1}=2, x_{2}=6,3 x_{1}+2 x_{2}=18 \leq 18$

Also $x_{1} \leq 4, x_{2} \leq 6$

$\therefore$ All conditions are satisfied.

$\therefore$ Maximum value of $\mathrm{Z}$ is $36 .$

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