In a linear programming problem, both the objective function and the constraints must be linear functions of the decision variables.Group of answer choicesTrueFalse
Question
In a linear programming problem, both the objective function and the constraints must be linear functions of the decision variables.Group of answer choicesTrueFalse
Solution 1
The correct answer is "True."
Explanation:
In a linear programming problem, both the objective function and the constraints are indeed linear functions of the decision variables. This means that each decision variable is only raised to the power of 1 and is not multiplied by any other decision variables. This linearity is what allows linear programming problems to be solved efficiently using methods like the Simplex algorithm. If either the objective function or the constraints are not linear, then the problem is not a linear programming problem and other methods must be used to solve it.
Solution 2
The correct answer is "True."
Explanation:
In a linear programming problem, both the objective function and the constraints are indeed linear functions of the decision variables. This means that each decision variable is only raised to the power of 1 and is not multiplied by any other decision variables. This linearity is what allows linear programming problems to be solved efficiently using methods like the Simplex algorithm. If either the objective function or the constraints are not linear, then the problem is not a linear programming problem and other methods must be used to solve it.
Solution 3
The correct answer is "True."
Explanation:
In a linear programming problem, both the objective function and the constraints are indeed linear functions of the decision variables. This means that each decision variable is only raised to the power of 1 and is not multiplied by any other decision variables. This linearity is what allows linear programming problems to be solved efficiently using methods like the Simplex algorithm. If either the objective function or the constraints are not linear, then the problem is not a linear programming problem and other methods must be used to solve it.
Solution 4
True.
In a linear programming problem, both the objective function and the constraints must be linear functions of the decision variables.
Here's why:
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Linear Objective Function: The objective function, which is the function to be maximized or minimized, must be a linear function of the decision variables. This means that each decision variable is only raised to the power of 1 and is not multiplied by any other decision variables.
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Linear Constraints: The constraints, which are the restrictions or limitations on the decision variables, must also be linear functions. This means that each constraint is a linear equation or inequality.
So, in a linear programming problem, both the objective function and the constraints must be linear functions of the decision variables.
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