12-18 Linear Programming Constraints

Front

What is the objective function in linear programming?

Back

The objective function is a mathematical expression that defines the goal of the optimization problem, typically in the form P = ax + by, where a and b are coefficients, and x and y are variables.

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How do you represent constraints in linear programming?

Back

Constraints in linear programming are represented as inequalities or equations that limit the values of the variables, such as 2x + 3y ≤ 18.

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What does the term 'feasible region' mean in linear programming?

Back

The feasible region is the set of all possible points that satisfy the constraints of a linear programming problem, typically represented graphically.

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What is the significance of corner points in linear programming?

Back

Corner points (or vertices) of the feasible region are significant because the optimal solution to a linear programming problem occurs at one of these points.

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Define the term 'variables' in the context of linear programming.

Back

Variables in linear programming are the unknowns that we are solving for, typically representing quantities that can be controlled, such as the number of items produced.

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What is the meaning of 'maximizing profit' in linear programming?

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Maximizing profit means finding the highest possible value of the objective function, which represents profit, given the constraints of the problem.

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How do you formulate an objective function from a word problem?

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To formulate an objective function, identify the quantities to be optimized (e.g., profit, cost) and express them in terms of the variables defined in the problem.

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What is a constraint in linear programming?

Back

A constraint is a condition that must be satisfied in a linear programming problem, often expressed as an inequality or equation.

Front

What does '2x + 3y ≤ 18' represent in a linear programming context?

Back

This inequality represents a constraint that limits the combination of variables x and y, indicating that the total contribution of 2 times x and 3 times y cannot exceed 18.

Front

What is the role of inequalities in linear programming?

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Inequalities define the boundaries of the feasible region and represent the limitations or restrictions on the variables.