Q57 / 150 · MHT CET 2023 (14 May Shift 1) · Mathematics

The solution set of the inequalities $4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$ is represented by region Figure

  • Correct answer
    A
    $\mathrm{S}_2$ region
  • B
    $\mathrm{S}_1$ region
  • C
    $\mathrm{S}_3$ region
  • D
    $\mathrm{S}_4$ region

Solution

Take a test point $(4,10)$ that lies within the $S_2$ region. $$ \begin{aligned} & \text { Since } 4(4)+3(10)=46 \leq 60,10 \geq 2(4)=8, \\ & 4 \geq 3,4 \geq 0,10 \geq 0 \end{aligned} $$ $\therefore \quad$ The solution set is represented by $\mathrm{S}_2$ region.

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

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