Linear Programming Day 2 Summative Assignment

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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How do you represent constraints in linear programming?

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Constraints in linear programming are represented as linear inequalities that define the feasible region for the solution.

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What does the feasible region represent in linear programming?

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

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What is the objective function in linear programming?

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The objective function is the equation that needs to be maximized or minimized in a linear programming problem.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

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What is the significance of the corner points in the feasible region?

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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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What is the difference between '≤' and '<' in inequalities?

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'≤' means 'less than or equal to', including the boundary, while '<' means 'less than', excluding the boundary.

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How do you set up a system of inequalities from a word problem?

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Identify the variables, determine the constraints from the problem, and express them as inequalities.

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What is the maximum capacity constraint in a linear programming problem?

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The maximum capacity constraint limits the total amount of resources or items that can be used or produced.

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What does it mean to maximize profit in a linear programming context?

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Maximizing profit means finding the combination of variables that yields the highest possible profit while satisfying all constraints.