Question

The correct constraints for the given feasible region are ..............

• A. $y - x \geq 1, x + 5y \leq 10, x + y \geq 2, x, y \geq 0$
• B. $y - x \leq 1, 2x + 5y \leq 10, x + y \geq 1, x, y \geq 0$
• C. $y - x \geq 1, 2x + 5y \leq 10, x + y \geq 1, x, y \geq 0$
• D. $x - y \leq 1, 2x + 5y \geq 10, x + y \leq 1, x, y \geq 0$

Hint:

Test the origin $(0,0)$ in the inequality to check which side is shaded.

Answer 1

The Correct Option is C

Step 1: Identify Line 1
Through $(0, 1)$ and $(-1, 0) \implies$ Equation is $y - x = 1$. Shaded region is above, so $y - x \geq 1$.
Step 2: Identify Line 2
Through $(5, 0)$ and $(0, 2) \implies \frac{x}{5} + \frac{y}{2} = 1 \implies 2x + 5y = 10$. Shaded is towards origin, so $2x + 5y \leq 10$.
Step 3: Identify Line 3
Through $(1, 0)$ and $(0, 1) \implies x + y = 1$. Shaded is away from origin, so $x + y \geq 1$.
Final Answer: (C)