The minimum value of $z = 2x_{1} + 3x_{2}$ subjected to the constraints $2x_{1} + 7x_{2} \geq 22,\ x_{1} + x_{2} \geq 6,\ \ 5x_{1} + x_{2} \geq 10$ and $x_{1},\ x_{2} \geq 0$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $z = 2x_{1} + 3x_{2}$
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At $D(0,\ 10)$
$z = 2(0) + 3(10) = 30$
At $B(1,\ 5)$
$z = 2(1) + 3(5) = 17$
At $A(4,\ 2)$
$z = 2(4) + 3(2) = 14$
At $C(11,\ 0)$
$z = 2(11) + 3(0) = 22$
The minimum value of $z$ is 14

Q. The minimum value of $z = 2x_{1} + 3x_{2}$ subjected to the constraints $2x_{1} + 7x_{2} \geq 22,\ x_{1} + x_{2} \geq 6,\ \ 5x_{1} + x_{2} \geq 10$ and $x_{1},\ x_{2} \geq 0$ is

Explanation

Reviewed by Dr. Abubacker

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