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If m is  the number of constraints in a linear programming with two variables x and y and non-negativity constraints x ≥ 0, y ≥ 0; the feasible region in the graphical solution will be surrounded by how many lines? 
  • a)
    m  
  • b)
    m  + 1  
  • c)
    m + 2  
  • d)
    m + 4 
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If m is the number of constraints in a linear programming with two var...
Constraints = 3 the feasible region is surrounded by more two lines x-axis and y-axis.
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Most Upvoted Answer
If m is the number of constraints in a linear programming with two var...
The feasible region in a linear programming problem represents the set of all possible solutions that satisfy the given constraints. In the case of a graphical solution with two variables, the feasible region is a bounded area on the coordinate plane.

To determine the number of lines that surround the feasible region, we need to consider the number of constraints in the problem.

Number of Constraints (m):
The number of constraints in a linear programming problem represents the number of inequalities or equations that define the constraints on the variables. In this case, the problem has 'm' constraints.

Feasible Region:
The feasible region is the area on the coordinate plane that satisfies all the constraints in the problem. Each constraint represents a line on the plane, and the feasible region is the intersection of all these lines.

Explanation:
Since we have two variables, x and y, and non-negativity constraints (x ≥ 0, y ≥ 0), we have two additional constraints in addition to the 'm' constraints given in the problem. These additional constraints represent the non-negativity region, which is the area where both x and y are greater than or equal to zero.

The non-negativity region is bounded by the x-axis (y = 0) and the y-axis (x = 0). These two lines are the boundaries of the feasible region in the graphical solution.

Therefore, the feasible region in the graphical solution of this problem will be surrounded by two lines - the x-axis and the y-axis.

Answer:
The correct answer is option 'C' - 2 lines.
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