The number of solutions of the system of inequations x+2y≤3,3x+4y≥12,x≥0 y≥1 is:

x+2y≤3 i.e. x≤3−2y3x+4y≥12 i.e. x≥4−4y/3therefore, 4−4y/3≤x≤3−2yTherefore, 4−4y/3≤3−2y2y−4y/3≤3−4y≤−3/2Since, y≥1So, there is no value of y satisfying these equations. Hence, no solution exist.

The number of solutions of the system of inequations x+2y≤3,3x+4y≥12,x≥0 y≥1 is:

x+2y≤3 i.e. x≤3−2y3x+4y≥12 i.e. x≥4−4y/3therefore, 4−4y/3≤x≤3−2yTherefore, 4−4y/3≤3−2y2y−4y/3≤3−4y≤−3/2Since, y≥1So, there is no value of y satisfying these equations. Hence, no solution exist.

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The number of solutions of the system of inequations $x + 2 y \leq 3, 3 x + 4 y \geq 12, x \geq 0$ $y \geq 1 is:$

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Detailed Solution

$\begin{aligned} x + 2 y \leq 3 \\ i.e. x \leq 3 - 2 y \\ 3 x + 4 y \geq 12 \\ i.e. x \geq 4 - 4 y / 3 \end{aligned}$
therefore, $4 - 4 y / 3 \leq x \leq 3 - 2 y$
Therefore, $4 - 4 y / 3 \leq 3 - 2 y$
$\begin{aligned} 2 y - 4 y / 3 \leq 3 - 4 \\ y \leq - 3 / 2 \end{aligned}$
Since, $y \geq 1$
So, there is no value of y satisfying these equations.
Hence, no solution exist.