Question

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

• A. $x, y \ge 0;\ x - y \ge 0;\ x \le 5;\ y \le 3$
• B. $x, y \ge 0;\ x - y \ge 0;\ x \le 5;\ y \ge 3$
• C. $x, y \ge 0;\ x + y \ge 0;\ x \ge 5;\ y \le 3$
• D. $x, y \ge 0;\ x - y \ge 0;\ x \ge 5;\ y \le 3$

Hint:

To pick out the correct constraints instantly, look at the outer flat limits. The region is blocked on the right at 5 and at the top at 3, so you must have $x \le 5$ and $y \le 3$. This allows you to eliminate options (B), (C), and (D) immediately without even testing the diagonal line!

Answer 1

The Correct Option is A

Step 1: Note the quadrant.
The shaded region is in the first quadrant, so $x \ge 0$ and $y \ge 0$.

Step 2: Read the straight boundaries.
The region is left of $x = 5$, so $x \le 5$, and below $y = 3$, so $y \le 3$.

Step 3: Read the slant line.
The slant line is $y = x$, and the region is below it, so $x - y \ge 0$. Testing $(4,1)$ gives $3 \ge 0$, which fits.
\[ \boxed{x,y \ge 0;\ x - y \ge 0;\ x \le 5;\ y \le 3,\ \text{option 1}} \]