Q95 / 150 · MHT CET 2021 (21 Sep Shift 1) · Mathematics

The shaded figure given below is the solution set for the linear inequations. Choose the correct option Figure

  • A
    $$ 3 x+4 y \geq 18 ; x-6 y \leq 3 ; 2 x+3 y \geq 3 ; 7 x-14 \leq 14 ; x \geq $$ $$ 0 ; \mathrm{y} \geq 0 $$
  • B
    $$ 3 x+4 y \leq 18 ; x-6 y \leq 3 ; 2 x+3 y \leq 3 ;-7 x+14 \geq 14 ; x \geq $$ $$ 0 ; \mathrm{y} \geq 0 $$
  • Correct answer
    C
    $$ \begin{aligned} & 3 x+4 y \leq 18 ; x-6 y \leq 3 ; 2 x+3 y \geq 3 ;-7 x+14 \leq 14 ; x \geq \\ & 0 ; y \geq 0 \end{aligned} $$
  • D
    $3 \mathrm{x}+4 \mathrm{y} \geq-18 ; \mathrm{x}-6 \mathrm{y} \leq 3 ; 2 \mathrm{x}+3 \mathrm{y} \leq 3 ;-7 \mathrm{x}+14 \geq 14 ; \mathrm{x} \geq 0 ; \mathrm{y} \geq 0$

Solution

For the shaded region, inequalities are as follows, $x \geq 0, y \geq 0,2 x+3 y \geq 3, x-6 y \leq 3,3 x+4 y \leq 18,-7 x+14 y \leq 14$ Note: $$ -7 x+14 y=14 \Rightarrow 7 x-14=-14 \text { and } 0>-14 $$

Hence, the correct answer is option: 'C'.

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