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 Linear Inequalities 24 Flashcards |
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Solve the inequality: 2x + 3y ≤ 12. What are the possible values of y when x = 0? |
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When x = 0, the inequality becomes 3y ≤ 12, which simplifies to y ≤ 4. Therefore, possible values of y are any number less than or equal to 4. |
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True or False: The solution set for the inequality x + y > 5 includes the point (2, 3). |
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True, because 2 + 3 = 5 does not satisfy the strict inequality, but points greater than (2, 3) do. |
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Fill in the blank: For the inequality 4x - y ≤ 8, if x = 2, then y must be ___ or greater. |
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Y must be 0 or greater, since 4(2) - y ≤ 8 simplifies to y ≥ 0. |
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What is the graphical representation of the inequality y ≤ 2x + 3? |
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The graph includes the line y = 2x + 3 and the area below this line, representing all points where y is less than or equal to 2x + 3. |
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If the constraints are 2x + y ≤ 10 and x + 2y ≤ 8, determine the feasible region. |
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The feasible region is the area on the graph where both inequalities are satisfied, typically shaded in the diagram. |
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Fill in the blank: The inequality 3x + 4y > 12 represents a region above the line defined by ___ when rewritten as an equation. |
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3x + 4y = 12. |
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Given the inequalities x + y ≤ 6 and x - y ≥ 2, find the intersection point. |
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To find the intersection point, solve the system: x + y = 6 and x - y = 2. The solution is (4, 2). |
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What does the term 'bounded' mean in the context of a feasible region? |
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A bounded feasible region is one that can be enclosed within a sufficiently large circle, meaning it does not extend to infinity. |
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Fill in the blank: The solution set of the inequality 5x + 3y ≤ 15 is represented graphically as the area ___ the line 5x + 3y = 15. |
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Below. |
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True or False: Increasing the coefficients in an objective function will always lead to a higher maximum value. |
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True, as increasing coefficients typically means a greater output for each unit of the variables. |
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If you have the inequality 6x + 2y < 18, what is the maximum possible value of y when x / > |
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Substituting x = 3 gives 6(3) + 2y < 18, which simplifies to 2y >< 0, so the maximum possible value of y is less than > |
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What is the significance of extreme points in a feasible region? |
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Extreme points are where the objective function achieves its maximum or minimum values, serving as crucial points for optimization. |
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