This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. It is the set of quantities that the decision makers would like to determine in order to solve the problem. A) Constraints. B) Decision variables. C) Variables. D) Parameter. Show Answer Correct Answer: B) Decision variables. 2. What is an objective function? A) A mathematical expression that defines the goal of a linear programming problem, typically to maximize or minimize a quantity. B) A type of function that only has one variable. C) A function that describes the relationship between two variables without any constraints. D) A function used to calculate the area under a curve. Show Answer Correct Answer: A) A mathematical expression that defines the goal of a linear programming problem, typically to maximize or minimize a quantity. 3. A linear programming model has the following two constraints:X1 $\geq$ 3 and X1 $\geq$ 4. This model has a redundant constraint. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 4. What does the feasible region represent in a linear programming graph? A) The feasible region shows only the optimal solution. B) The feasible region indicates the constraints that are not met. C) The feasible region represents all possible solutions that satisfy the constraints. D) The feasible region represents all possible solutions without any constraints. Show Answer Correct Answer: C) The feasible region represents all possible solutions that satisfy the constraints. 5. Sarah makes $ 30 for each small purse (x) and $ 50 for each big purse (y). Which expression can be used to determine the cost (this is called the objective quantity)? A) 30x + 50y. B) 50x + 30y. C) All the above. D) None of the above. Show Answer Correct Answer: A) 30x + 50y. 6. What is the role of the origin in the graphical method of linear programming? A) The origin is irrelevant in the graphical method of linear programming. B) The origin serves as a reference point for determining the feasible region and optimal solution. C) The origin represents the maximum value in linear programming. D) The origin is used to plot the constraints in linear programming. Show Answer Correct Answer: B) The origin serves as a reference point for determining the feasible region and optimal solution. 7. Graph the inequality 3x + 4y < 24 on a coordinate plane. A) Graph a solid line through points (8, 0) and (0, 6) and shade above the line. B) Graph the dashed line through points (6, 0) and (0, 8) and shade above the line. C) Graph a solid line through points (0, 6) and (0, 0) and shade below the line. D) Graph the dashed line through points (8, 0) and (0, 6) and shade below the line. Show Answer Correct Answer: D) Graph the dashed line through points (8, 0) and (0, 6) and shade below the line. 8. If Zj-Cj<0 then the dual simplex method ..... A) Basic feasible. B) Pseudo optimal. C) Fails. D) Feasible. Show Answer Correct Answer: C) Fails. 9. What does it mean if a point is on the boundary of the feasible region? A) A point on the boundary is not considered feasible. B) A point on the boundary does not satisfy any constraints. C) A point on the boundary satisfies at least one of the constraints. D) A point on the boundary is always an optimal solution. Show Answer Correct Answer: C) A point on the boundary satisfies at least one of the constraints. 10. In the context of Linear Programming, what does the term 'feasible region' refer to? A) The area where costs are minimized. B) The area where resources are abundant. C) The area where profits are maximized. D) The area where all constraints are satisfied. Show Answer Correct Answer: D) The area where all constraints are satisfied. 11. The constraint 2x1-x2 = 0 passes through the point (200, 100).6. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 12. How do we show a straight line on a graph? A) Draw a circle around the y-intercept. B) Plot the y-intercept and use the slope to draw the line. C) Connect random points on the graph. D) Use only the x-axis to represent the line. Show Answer Correct Answer: B) Plot the y-intercept and use the slope to draw the line. 13. What are the components of a linear programming model? A) Objective function, Decision variables, Assumptions, Parameters. B) Objective function, Decision variables, Constraints, Parameters. C) Objective function, Constraints, Parameters, Right-hand side values. D) Objective function, Decision variables, Constraints, Assumptions. Show Answer Correct Answer: B) Objective function, Decision variables, Constraints, Parameters. 14. How can you verify if a solution is optimal in a graphical method? A) Check if the solution is on the boundary of the feasible region and is the best value. B) Ensure the solution is the first point found in the graph. C) Verify if the solution is in the interior of the feasible region. D) Check if the solution is a random point in the graph. Show Answer Correct Answer: A) Check if the solution is on the boundary of the feasible region and is the best value. 15. Graph the inequality x + 2y > 10 and identify the feasible region. A) The feasible region is the area below the line x + 2y = 10, excluding the line. B) The feasible region is the area above the line x + 2y = 10, including the line. C) The feasible region is the area to the left of the line x + 2y = 10, excluding the line. D) The feasible region is the area to the right of the line x + 2y = 10, including the line. Show Answer Correct Answer: B) The feasible region is the area above the line x + 2y = 10, including the line. 16. In a LPP, the linear inequalities or restrictions on the variables are called ..... A) Linear constraints. B) Quadratic constraints. C) Cubic constraints. D) None of these. Show Answer Correct Answer: A) Linear constraints. 17. The graph of y > 23x-48uses a ..... line A) Dashed. B) Vertical. C) Horizontal. D) Solid. Show Answer Correct Answer: A) Dashed. 18. What is the inequality for CUTTING TIME? A) 2x + 3y < 24. B) 2x + 3y < 36. C) 6x + 3y < 24. D) 6x + 3y < 36. Show Answer Correct Answer: A) 2x + 3y < 24. 19. To find the optimal solution to a linear programming problem using the graphical method, find the feasible point that13. A. is the farthest away from the origin.B. is at the highest location.C. is closest to the origin.D. provides the best possible value of the objective function. A) B. B) D. C) A. D) C. Show Answer Correct Answer: B) D. 20. How does linear programming contribute to cost reduction in forest-based industries? A) By minimizing production output. B) By optimizing resource usage. C) By increasing harvesting costs. D) By maximizing inventory holding costs. Show Answer Correct Answer: B) By optimizing resource usage. 21. The common region represented by $x\le4$ $x-y\ge0$ $3x+y\ge3$ A) First quadrant. B) First and second quadrants. C) Third quadrant. D) First and fourth quadrants. Show Answer Correct Answer: D) First and fourth quadrants. 22. What does the objective function in linear programming represent? A) The goal of the firm. B) The number of employees needed. C) The amount of resources available. D) The total cost of production. Show Answer Correct Answer: A) The goal of the firm. 23. What is the main benefit of using GeoGebra in teaching graphical solutions? A) To discourage student participation. B) To increase student workload. C) To complicate the learning process. D) To simplify complex concepts. Show Answer Correct Answer: D) To simplify complex concepts. 24. When feasible region is such that feasible solution can extend to infinity, it is called A) Infinite. B) The vast open sky. C) Infeasible. D) Unbounded. Show Answer Correct Answer: D) Unbounded. 25. The vertices of a feasible region are (4, 12), (0, 9), (6, 8), and (10, 3). Find themaximum value of P if P = 80x + 20y? A) 890. B) 860. C) 840. D) 880. Show Answer Correct Answer: B) 860. 26. How can linear programming be applied in manufacturing companies? A) Managing human resources. B) Optimizing production planning. C) Forecasting market trends. D) Analyzing financial statements. Show Answer Correct Answer: B) Optimizing production planning. 27. What does the term 'unbounded solution' refer to in linear programming? A) A solution that has no constraints. B) A solution that is always feasible. C) A solution that cannot be determined. D) A solution that can increase indefinitely. Show Answer Correct Answer: D) A solution that can increase indefinitely. 28. In a maximization LPP, the value of the objective function: A) Is unaffected by constraints. B) Remains the same. C) Increases in the feasible region. D) Always decreases. Show Answer Correct Answer: C) Increases in the feasible region. 29. How can LP be applied in healthcare? A) To optimize staff scheduling. B) None of the above. C) To manage investment portfolios. D) To plan crop rotations. Show Answer Correct Answer: C) To manage investment portfolios. 30. What is an optimal solution in linear programming? A) The solution that only satisfies the constraints without optimizing the objective. B) A solution that is not feasible for the problem. C) Any random point in the solution space. D) The best feasible solution that maximizes or minimizes the objective function. Show Answer Correct Answer: D) The best feasible solution that maximizes or minimizes the objective function. 31. What is the purpose of scenario analysis in LP using Microsoft Excel? A) To confuse students. B) To complicate the process. C) To avoid solving problems. D) To explore different scenarios and evaluate their impact. Show Answer Correct Answer: D) To explore different scenarios and evaluate their impact. 32. Question 1:In a linear programming problem, what does the feasible region represent? A) Set of impossible solutions. B) Set of all possible solutions that satisfy the constraints and are within the bounds of the problem. C) Set of solutions that violate the constraints. D) Set of solutions that are outside the bounds of the problem. Show Answer Correct Answer: B) Set of all possible solutions that satisfy the constraints and are within the bounds of the problem. 33. Usage of linear and nonlinear equations and inequalities A) Maximum profit point. B) Intersection of the profit line and a constraint. C) Corner point. D) Intersection of two or more constraints. E) None of the above. Show Answer Correct Answer: E) None of the above. 34. How do you interpret the solution set of a linear programming problem? A) The solution set is limited to integer values only. B) The solution set only includes the optimal solution. C) The solution set represents all possible outcomes regardless of constraints. D) The solution set includes all feasible solutions that meet the constraints. Show Answer Correct Answer: D) The solution set includes all feasible solutions that meet the constraints. 35. Which vertex yields the highest profit? A) (6, 0). B) (3, 6). C) (0, 0). D) (0, 8). Show Answer Correct Answer: B) (3, 6). 36. What is the main benefit of LP in optimizing supply chain operations? A) To complicate operations. B) To determine cost-effective transportation. C) To increase costs. D) To slow down production. Show Answer Correct Answer: B) To determine cost-effective transportation. 37. Which type of non-linear function is often found in cost and revenue models in supply chains, involving terms like x2? A) Exponential Functions. B) Quadratic Functions. C) Concave Functions. D) Logarithmic Functions. Show Answer Correct Answer: B) Quadratic Functions. 38. Adding a constraint to a linear programming problem increases the size of the feasible region. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 39. A feasible solution is said to be an ..... solution if it minimizes the total transportationcost A) Feasible. B) Non degenerate basic feasible. C) Optimal. D) Basic feasible. Show Answer Correct Answer: C) Optimal. 40. What is the key idea behind the graphical method of solving LP problems? A) Ignoring constraints. B) Guessing solutions. C) Plotting constraints to visually represent the feasible region. D) Avoiding graphs. Show Answer Correct Answer: C) Plotting constraints to visually represent the feasible region. 41. In an LPP, decision variables are: A) Unknowns to be determined. B) Constant values. C) Objective functions. D) Fixed coefficients. Show Answer Correct Answer: A) Unknowns to be determined. 42. It is a method for finding a maximum or minimum value of some quantity, given a set of constraints. A) Operations research. B) Minimization. C) Linear programming. D) Maximization. Show Answer Correct Answer: C) Linear programming. 43. Solve the system by substitution. 2x-y =-5 y = 2x + 5 A) Infinite number of solutions. B) (-4, 3). C) (-4, 5). D) (-4, -8). Show Answer Correct Answer: A) Infinite number of solutions. 44. What are the main components of a linear programming model? A) Objective function, decision variables, constraints, non-negativity restrictions. B) Decision-making process, feedback loops, data analysis, forecasting. C) Cost-benefit analysis, stakeholder engagement, project management, performance metrics. D) Profit maximization, resource allocation, market analysis, risk assessment. Show Answer Correct Answer: A) Objective function, decision variables, constraints, non-negativity restrictions. 45. Solve the optimization problem:Maximize 4x + 3y subject to the constraints x >= 0, y >= 0, and x + y <= 5. A) 15. B) 7. C) 10. D) 20. Show Answer Correct Answer: D) 20. 46. Identify each of the following system of linear equations as having no solution, one solution, or infinitely many solutions. $2x+4y=14$ $6x+12y=42$ A) No solutions. B) Two solutions. C) Infinitely many solutions. D) One solution. Show Answer Correct Answer: C) Infinitely many solutions. 47. What do we call the things we want to find in a problem? A) Equations. B) Constants. C) Variables. D) Parameters. Show Answer Correct Answer: C) Variables. 48. ..... are the restrictions or limitation imposed on the linear programming problem. A) Profit. B) Constraints. C) Variables. D) Cost. Show Answer Correct Answer: B) Constraints. 49. In the Beaver Creek example, what is the profit per unit for a bowl? A) $ 40. B) $ 20. C) $ 30. D) $ 50. Show Answer Correct Answer: A) $ 40. 50. What is the goal of prescriptive analytics? A) Make a recommendation on an action that will optimize a goal. B) Explain the relationship between actions and outcomes. C) Optimize a function. D) Develop a model to describe the data. Show Answer Correct Answer: A) Make a recommendation on an action that will optimize a goal. 51. Determine if the system of equations 2x + 3y = 5 and 4x + 6y = 10 is consistent. A) The system has infinitely many solutions. B) The system is consistent. C) The system has no solutions. D) The system is inconsistent. Show Answer Correct Answer: B) The system is consistent. 52. What is the assumption of linearity in linear programming models? A) Parameters are known and constant. B) Negative values of variables are unrealistic. C) Non-integer values are acceptable. D) Each decision variable has a linear impact on the objective function and constraints. Show Answer Correct Answer: D) Each decision variable has a linear impact on the objective function and constraints. 53. Solve using elimination:x-y=112x+y=19 A) (-1, 10). B) (6, 7). C) (10, -1). D) (3, -4). Show Answer Correct Answer: C) (10, -1). 54. In linear programming, what are decision variables? A) Variables that are always negative. B) Variables that can take any value. C) Variables that are only integers. D) Variables that are non-negative. Show Answer Correct Answer: D) Variables that are non-negative. 55. What is the primary focus of Session 10.4? A) Teaching Statistics. B) Teaching Linear Programming. C) Teaching Algebra. D) Teaching Calculus. Show Answer Correct Answer: B) Teaching Linear Programming. 56. The optimal solution to any linear programming problem is at A) The origin. B) A corner point of the feasible region. C) The lowest point in the feasible region. D) None of the above. Show Answer Correct Answer: B) A corner point of the feasible region. 57. What is the first step in solving a linear programming problem graphically? A) Graph the objective function first. B) Calculate the objective function value. C) Choose a random point in the feasible region. D) Identify the constraints and express them as inequalities. Show Answer Correct Answer: D) Identify the constraints and express them as inequalities. 58. Alternative optimal solutions occur when there is no feasible solution to the problem.8. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 59. A constraint has a slack of 5 units. This implies that: A) This constraint has exceeded its minimal requirement by 5 units. B) This constraint has consumed 5 units of its resource. C) This constraint has a surplus of 5 units. D) This constraint is binding. E) This constraint has 5 units of its resource unconsumed. Show Answer Correct Answer: E) This constraint has 5 units of its resource unconsumed. 60. A controllable input for a linear programming model is known as a A) Dummy variable. B) Decision variable. C) Parameter. D) Constraint. Show Answer Correct Answer: B) Decision variable. 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