Find the feasible region $x - 2y 0$, $x 2$, $y 1$, $x + y 6$, $3x + 4y 28$ Is $(2, 1)$, $(2.5, 1)$ feasible. Sol?See answer

Daftar Isi

Find the feasible region x 2y 0 x 2 y 1 x y 6 3x 4y 28 Is 2 1 25 1 feasible Sol

Question

Find the feasible region $x – 2y \ge 0$, $x \le 2$, $y \ge 1$, $x + y \ge 6$, $3x + 4y \le 28$ Is $(2, 1)$, $(2.5, 1)$ feasible. Sol?

Basic Answer

Step 1: Identify the constraints

We have the following constraints:

1. $x-2y\ge 0$
2. $x\le 2$
3. $y\ge 1$
4. $x+y\ge 6$
5. $3x+4y\le 28$

Step 2: Check if $(2,1)$ is feasible

1. $x-2y\ge 0$: $2-2(1)=2-2=0$ (True)
2. $x\le 2$: $2\le 2$ (True)
3. $y\ge 1$: $1\ge 1$ (True)
4. $x+y\ge 6$: $2+1=3\ge 6$ (False)
5. $3x+4y\le 28$: $3(2)+4(1)=6+4=10\le 28$ (True)

Since $x+y\ge 6$ is not satisfied, $(2,1)$ is not feasible.

Step 3: Check if $(2.5,1)$ is feasible

1. $x-2y\ge 0$: $2.5-2(1)=2.5-2=0.5\ge 0$ (True)
2. $x\le 2$: $2.5\le 2$ (False)
3. $y\ge 1$: $1\ge 1$ (True)
4. $x+y\ge 6$: $2.5+1=3.5\ge 6$ (False)
5. $3x+4y\le 28$: $3(2.5)+4(1)=7.5+4=11.5\le 28$ (True)

Since $x\le 2$ and $x+y\ge 6$ are not satisfied, $(2.5,1)$ is not feasible.

Final Answer

Neither $(2,1)$ nor $(2.5,1)$ are feasible points.