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11. ⇒ (MHT CET 2021 20th September Evening Shift )

The solution set for the system of linear inequations $x + y \geq 1; 7 x + 9 y \leq 63; y \leq 5; x \leq 6, x \geq 0$ and $y \geq 0$ is represented graphically in the figure. What is the correct option?

A. MHT CET 2021 20th September Evening Shift Mathematics - Linear Programming Question 11 English Option 1

B. MHT CET 2021 20th September Evening Shift Mathematics - Linear Programming Question 11 English Option 2

C. MHT CET 2021 20th September Evening Shift Mathematics - Linear Programming Question 11 English Option 3

D. MHT CET 2021 20th September Evening Shift Mathematics - Linear Programming Question 11 English Option 4

Correct answer option is (A)

Lines are $x + y = 1, 7 x + 9 y = 63, y = 5, x = 6$

The required area is shaded.

MHT CET 2021 20th September Evening Shift Mathematics - Linear Programming Question 11 English Explanation

12. ⇒ (MHT CET 2021 20th September Morning Shift )

The shaded part of the given figure indicates the feasible region. Then the constraints are

MHT CET 2021 20th September Morning Shift Mathematics - Linear Programming Question 12 English

A. $x, y \geq 0; x - y \geq 0; x \leq 5; y \leq 3$

B. $x, y \geq 0; x - y \geq 0; x \leq 5; y \geq 3$

C. $x, y \geq 0; x + y \geq 0; x \geq 5; y \leq 3$

D. $x, y \geq 0; x - y \geq 0; x \geq 5; y \leq 3$

Correct answer option is (A)

Here equation of line OC is $y = x$ i.e. $x - y = 0$ and equation of line AB is $x = 5$ i.e. $x - 5 = 0$

Equation of line BC is $y = 3$ i.e. $y - 3 = 0$

Hence constraints for the shaded region are $x, y \geq 0, x - 5 \leq 0, x - y \geq 0, y - 3 \leq 0$ i.e. $x, y \geq 0, x \leq 5, x - y \geq 0, y \leq 3$

⇒Linear programming