Of the following, which group of constraints represents the feasible region given below?
Of the following, which group of constraints represents the feasible region given below?
Show Hint
- \( x + 2y \leq 76, \, 2x + y \geq 104, \, x, y \geq 0 \)
- \( x + 2y \leq 76, \, 2x + y \leq 104, \, x, y \geq 0 \)
- \( x + 2y \geq 76, \, 2x + y \leq 104, \, x, y \geq 0 \)
- \( x + 2y \geq 76, \, 2x + y \geq 104, \, x, y \geq 0 \)
The Correct Option is C
Solution and Explanation
To determine the correct constraints, analyze the feasible region depicted in the graph:
1. Line 1: \( x + 2y = 76 \) The region above this line is shaded, indicating the constraint: \[ x + 2y \geq 76. \] 2. Line 2: \( 2x + y = 104 \) The region below this line is shaded, indicating the constraint: \[ 2x + y \leq 104. \] 3. Non-negativity constraints: Since the shaded region is in the first quadrant: \[ x \geq 0 \quad {and} \quad y \geq 0. \] Thus, the group of constraints representing the feasible region is: \[ x + 2y \geq 76, \, 2x + y \leq 104, \, x \geq 0, \, y \geq 0. \]
Final Answer: \( \boxed{{(C)}} \)
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