This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 8 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 8 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If x1 + x2 is less than or equal to 500y1 and y1 is 0-1, then x1 and x2 will be ..... if y1 is 0. A) Equal to 0. B) More than 0. C) Less than 0. D) Equal to 500. Show Answer Correct Answer: A) Equal to 0. 2. In a Linear Programming model, what do constraints represent? A) The limitations on resources. B) The objective function. C) The profit margins. D) The decision variables. Show Answer Correct Answer: A) The limitations on resources. 3. Which of the following variable is not considered in LPP? A) Slack Variable. B) Random Variable. C) Surplus Variable. D) Artificial Variable. Show Answer Correct Answer: B) Random Variable. 4. What is the key idea behind finding the optimal solution in LP problems? A) The optimal solution is always at the center of the feasible region. B) The optimal solution is not important in LP problems. C) The optimal solution is found at the intersection of constraints. D) The optimal solution is randomly determined. Show Answer Correct Answer: C) The optimal solution is found at the intersection of constraints. 5. In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses? A) 10 horses, 18 chickens. B) 18 horses, 10 chickens. C) 16 horses, 12 chickens. D) 12 horses, 16 chickens. Show Answer Correct Answer: D) 12 horses, 16 chickens. 6. When no solution to the linear programming problem satisfies all the constraints, including the nonnegativity conditions, it is considered12. A. optimal.B. feasible.C. infeasible.D. semifeasible. A) D. B) A. C) C. D) B. Show Answer Correct Answer: C) C. 7. What is the value of the objective function at the point (6, 0)? A) 12. B) 15. C) 24. D) 18. Show Answer Correct Answer: C) 24. 8. Which of the following is true about the feasible region in a linear programming problem? A) It is always a line. B) It is the intersection of all constraints. C) It is the union of all constraints. D) It is always unbounded. Show Answer Correct Answer: B) It is the intersection of all constraints. 9. If an LPP has no solution, it is called: A) Redundant. B) Degenerate. C) Feasible. D) Infeasible. Show Answer Correct Answer: D) Infeasible. 10. In the context of Linear Programming, what does 'redundant constraint' mean? A) A constraint that does not affect the solution. B) A constraint that is contradictory. C) A constraint that limits the solution space. D) A constraint that is always satisfied. Show Answer Correct Answer: A) A constraint that does not affect the solution. 11. Which of the following statements is correct about a redundant constraint?16. A. A redundant constraint affects the optimal solution.B. A redundant constraint affects the feasible region.C. Recognizing a redundant constraint is not possible with the graphical solution.D. At the optimal solution, a redundant constraint will have zero slack. A) A. B) D. C) B. D) C. Show Answer Correct Answer: B) D. 12. In LP, what do constraints represent? A) Environmental impact. B) Limitations on decision variables. C) Resources to be optimized. D) Objectives to be achieved. Show Answer Correct Answer: B) Limitations on decision variables. 13. Identify each of the following system of linear equations as having no solution, one solution, or infinitely many solutions. $12x+9y=8$ $4x+3y=5$ A) One solution. B) Two solutions. C) Infinitely many solutions. D) No solutions. Show Answer Correct Answer: D) No solutions. 14. Which of the following statements is true about matrix multiplication? A) Matrix multiplication is commutative. B) Matrix multiplication is associative. C) Matrix multiplication is neither commutative nor associative. D) Matrix multiplication is commutative and associative. Show Answer Correct Answer: B) Matrix multiplication is associative. 15. What is the purpose of introducing slack variables in the simplex method? A) To determine the leaving variable. B) To convert inequalities into equations. C) To improve the initial feasible solution. D) To identify the entry variable. Show Answer Correct Answer: B) To convert inequalities into equations. 16. Second step in formulating Linear Programming A) Identify the objective and constraints. B) Define the decision variables. C) Completely understand the managerial problem being faced. D) Use the decision variables to write mathematical expressions for the objective function and the constraints. Show Answer Correct Answer: A) Identify the objective and constraints. 17. Solve the linear programming problem:Minimize z = 2x + 3y subject to 3x + 4y $\geq$ 12, x $\geq$ 0, y $\geq$ 0. A) 8. B) 12. C) 5. D) 10. Show Answer Correct Answer: A) 8. 18. What does a feasible solution in linear programming imply? A) It violates at least one constraint. B) It satisfies all constraints. C) It is not possible to determine. D) It is the optimal solution. Show Answer Correct Answer: B) It satisfies all constraints. 19. Graph the linear equation 2x + 3y = 12. A) Y = (3/2)x-6. B) Y = (-3/2)x + 6. C) Y = (2/3)x-4. D) Y = (-2/3)x + 4. Show Answer Correct Answer: D) Y = (-2/3)x + 4. 20. Graph the linear equation 5x-y = 10. A) Y = 10-5x. B) Y = 5x + 10. C) Y = 5x-10. D) Y =-5x-10. Show Answer Correct Answer: C) Y = 5x-10. 21. An ..... solution violates "at least one" constraint. A) Infeasible. B) Good. C) Bad. D) Feasible. Show Answer Correct Answer: A) Infeasible. 22. What is the main focus of linear programming? A) Integrating rational functions. B) Solving trigonometric equations. C) Optimizing a linear function. D) Differentiating polynomials. Show Answer Correct Answer: C) Optimizing a linear function. 23. In the context of financial planning for a startup, what is meant by non-negative restrictions? A) Constraints that require all budget items to be greater than a certain positive value. B) Constraints that prevent the financial balance from taking negative values. C) Constraints that require all budgetary decision variables to be non-negative. D) Constraints that limit the number of budget items that can take positive values. Show Answer Correct Answer: C) Constraints that require all budgetary decision variables to be non-negative. 24. A special case which happens only on minimization problems A) Infeasibility. B) Alternate solutions. C) Redundancy. D) Unboundedness. Show Answer Correct Answer: D) Unboundedness. 25. What is the first step in developing a linear programming model? A) Solution of the model. B) Interpretation of results. C) Formulation of the mathematical model. D) Identification of the problem. Show Answer Correct Answer: D) Identification of the problem. 26. It uses formula and expressions to represent a problem. A) Imitation. B) Linear. C) Symbolic. D) None of the above. Show Answer Correct Answer: C) Symbolic. 27. How does GeoGebra help in teaching the graphical method of solving linear programming problems? A) By providing interactive visualization capabilities. B) By solving problems automatically. C) By printing out solutions. D) By generating random graphs. Show Answer Correct Answer: A) By providing interactive visualization capabilities. 28. What is the significance of corner points in the graphical method? A) Corner points are used to determine the slope of the graph. B) Corner points only represent infeasible solutions. C) Corner points are significant as they represent potential optimal solutions in linear programming. D) Corner points are irrelevant in linear programming. Show Answer Correct Answer: C) Corner points are significant as they represent potential optimal solutions in linear programming. 29. What is the minimum value of the objective function in the given linear programming problem? A) 15. B) 24. C) 18. D) 12. Show Answer Correct Answer: A) 15. 30. If a function has no maximum value, the shaded regions of the constraints are ..... since they do not form a closed figure. A) Feasible. B) Unbounded. C) Objective. D) Linear. Show Answer Correct Answer: B) Unbounded. 31. What do the vertices of the feasible region represent? A) Graphing Errors. B) Irrelevant Information. C) Random Data Points. D) Key Points for Sensitivity Analysis. Show Answer Correct Answer: D) Key Points for Sensitivity Analysis. 32. What are restrictions in a Linear Programming Problem called? A) Variable. B) Profit. C) Constraints. D) As if I can be bothered with this. Show Answer Correct Answer: C) Constraints. 33. Which key characteristic of an NLP problem makes finding the absolute best solution difficult? A) Non-Linearity in Objective Function. B) Use of the Lagrange Multipliers method. C) Continuous Variables. D) Multiple Local Optima. Show Answer Correct Answer: D) Multiple Local Optima. 34. Which of the following is a constraint in a linear programming problem? A) Profit maximization. B) Objective function. C) Variable definition. D) Resource limitation. Show Answer Correct Answer: D) Resource limitation. 35. A transportation problem can always be represented by balanced model. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 36. In the graphical method, the optimal solution lies: A) Inside the feasible region. B) Outside the feasible region. C) At the origin. D) At a corner (vertex) of the feasible region. Show Answer Correct Answer: D) At a corner (vertex) of the feasible region. 37. Solve by matrices. $4x + 9y = 28$ $-4x-y =-28$ A) (6, 0). B) (7, 0). C) (-6, 0). D) (-7, 0). Show Answer Correct Answer: B) (7, 0). 38. The first step in formulating an LP problem is A) Graph the problem. B) Perform a sensitivity analysis. C) Identify the objective and the constraints. D) Understand the managerial problem being faced. E) Define the decision variables. Show Answer Correct Answer: D) Understand the managerial problem being faced. 39. How is the optimal solution determined in linear programming? A) By maximizing or minimizing the objective function while satisfying all constraints. B) By ignoring the constraints and focusing only on the objective function. C) By randomly selecting values for the decision variables. D) By choosing the most complex solution. Show Answer Correct Answer: A) By maximizing or minimizing the objective function while satisfying all constraints. 40. Which method for solving NLP problems follows the steepest descent of the objective function to find a local optimum? A) Lagrange Multipliers. B) Gradient Descent. C) Simplex Method. D) Interior-Point Method. Show Answer Correct Answer: B) Gradient Descent. 41. In linear programming the constraints can be linear, quadratic, or cubic. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 42. What happens if the feasible region in the graphical method is unbounded? A) The problem is unsolvable. B) The solution is unique. C) There is no optimal solution. D) The method is invalid. Show Answer Correct Answer: C) There is no optimal solution. 43. How do you determine which side of the line to shade when graphing an inequality? A) Pick a test point not on the line and substitute its coordinates into the inequality. If the inequality is true, shade the side where the test point lies; if false, shade the other side. B) Shade both sides of the line. C) Always shade the left side of the line. D) Choose the side with the higher numbers. Show Answer Correct Answer: A) Pick a test point not on the line and substitute its coordinates into the inequality. If the inequality is true, shade the side where the test point lies; if false, shade the other side. 44. What role do decision variables play in linear programming? A) Decision variables are the final results of the optimization process. B) Decision variables are the unknowns that the model seeks to determine for optimization. C) Decision variables are the constants used in the model. D) Decision variables represent the constraints of the problem. Show Answer Correct Answer: B) Decision variables are the unknowns that the model seeks to determine for optimization. 45. And four destinations will have seven decision variables. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 46. What does the graphical method of solving linear programming problems involve? A) Plotting constraints on a graph. B) Solving equations algebraically. C) Drawing random lines. D) Using trial and error method. Show Answer Correct Answer: A) Plotting constraints on a graph. 47. What role do constraints play in linear programming? A) Constraints define the feasible region and ensure solutions meet specific requirements. B) Constraints are used to maximize the objective function. C) Constraints are optional and can be ignored in linear programming. D) Constraints limit the number of variables in the model. Show Answer Correct Answer: A) Constraints define the feasible region and ensure solutions meet specific requirements. 48. Which of the following methods is commonly used to solve linear programming problems? A) Graphical method. B) Trial and error. C) None of the above. D) Random search. Show Answer Correct Answer: A) Graphical method. 49. Which method is used for solving LPP with more than two variables? A) Graphical method. B) Simplex method. C) Trial and error. D) None. Show Answer Correct Answer: B) Simplex method. 50. Which method is useful for problems with two variables in linear programming? A) Simplex Method. B) Graphical Method. C) Diet Problems. D) Resource Allocation. Show Answer Correct Answer: B) Graphical Method. 51. What are the key components of a linear programming problem? A) Objective function, decision variables, non-negativity constraints. B) Objective function, decision variables, constraints, non-negativity constraints. C) Variables, constraints, objective function. D) Constraints, objective function, non-negativity constraints. Show Answer Correct Answer: B) Objective function, decision variables, constraints, non-negativity constraints. 52. Redundancy causes major difficulties to an LP problem. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 53. A non degenerated basics feasible solution all m variable are positive and remaining are A) 1. B) Zero. C) 2. D) None of above. Show Answer Correct Answer: B) Zero. 54. These are raw facts, symbols and figures A) DATA. B) DATABASE. C) DATA WAREHOUSE. D) INFORMATION. Show Answer Correct Answer: A) DATA. 55. When graphing a system of linear inequalities, how do you identify the feasible region? A) Select the region with the highest slope. B) Shade the overlapping or intersecting region. C) Color the region outside the feasible area. D) Highlight the area with the smallest y-intercept. Show Answer Correct Answer: B) Shade the overlapping or intersecting region. 56. In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 57. What does the feasible region represent in a business optimization problem involving linear programming? A) The set of all possible solutions that satisfy the profit maximization function. B) The set of all possible solutions that do not satisfy the budgetary constraints. C) The set of all possible solutions that satisfy the budgetary constraints. D) The optimal solution to the business optimization problem. Show Answer Correct Answer: C) The set of all possible solutions that satisfy the budgetary constraints. 58. In an L.P., the allowed numbers of constraints are: A) Unlimited. B) Zero. C) Two. D) Ten. Show Answer Correct Answer: A) Unlimited. 59. What tool can be used to find the optimal point in GeoGebra? A) Erase Tool. B) Zoom Tool. C) Intersect Tool. D) Highlight Tool. Show Answer Correct Answer: C) Intersect Tool. 60. Where can the coordinates of the optimal point be found using GeoGebra? A) By using the Intersect tool. B) By drawing random shapes. C) By guessing the coordinates. D) By using the Fill tool. Show Answer Correct Answer: A) By using the Intersect tool. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 12 Linear Programming Quiz 1Class 12 Mathematics Chapter 12 Linear Programming Quiz 2Class 12 Mathematics Chapter 12 Linear Programming Quiz 3Class 12 Mathematics Chapter 12 Linear Programming Quiz 4Class 12 Mathematics Chapter 12 Linear Programming Quiz 5Class 12 Mathematics Chapter 12 Linear Programming Quiz 6Class 12 Mathematics Chapter 12 Linear Programming Quiz 7Class 12 Mathematics Chapter 12 Linear Programming Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books