This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 10 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 10 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following is an application of linear programming? A) Scheduling school buses. B) Planning a birthday party. C) Choosing a vacation destination. D) Deciding on a movie to watch. Show Answer Correct Answer: A) Scheduling school buses. 2. Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. What is the objective function? A) M = 3x + 10y. B) M = 100x + 20y. C) M = 10x + 3y. D) M = 20x + 100y. Show Answer Correct Answer: D) M = 20x + 100y. 3. In dual simplex method, the starting solution is ..... A) Feasible. B) Not feasible. C) All the above. D) None of the above. Show Answer Correct Answer: B) Not feasible. 4. Why is it important to find the vertices of the feasible region? A) To calculate the average. B) To solve a linear programming problem. C) To find the midpoint. D) To determine the distance. Show Answer Correct Answer: B) To solve a linear programming problem. 5. The number of constraints in dual is equal to number of variables in primal. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 6. What are some real-world applications of linear programming? A) Weather forecasting. B) Website design. C) Applications of linear programming include resource allocation, production scheduling, transportation optimization, and financial portfolio design. D) Social media marketing. Show Answer Correct Answer: C) Applications of linear programming include resource allocation, production scheduling, transportation optimization, and financial portfolio design. 7. What is the first step in applying linear programming? A) Identify the problem. B) Implement the solution. C) Formulate the constraints. D) Solve the model. Show Answer Correct Answer: A) Identify the problem. 8. Where is the optimal solution of a linear programming problem typically found? A) At the corner points of the feasible region. B) At the center of the graph. C) At the intersection of two random lines. D) At the origin of the coordinate system. Show Answer Correct Answer: A) At the corner points of the feasible region. 9. A department store sells perfume and cologne. ~The store sells at least 2 bottles of perfume a day, but no more than 25.~The store sells more than 3 bottles of cologne, but less than 20 a day. Which of the following would represent one of the constraints for the feasible region? A) $2 B) $20\le y\le25$. C) $2\le x\le25$. D) $3\le y\le20$. Show Answer Correct Answer: C) $2\le x\le25$. 10. What is the first step in solving LP problems using Microsoft Excel? A) Input Decision Variables and Constraints. B) Define the Objective Function. C) Interpret the Results. D) Run the Solver Tool. Show Answer Correct Answer: A) Input Decision Variables and Constraints. 11. How can manufacturing companies benefit from graphical solutions in linear programming? A) Optimizing financial reporting. B) Optimizing production planning. C) Optimizing customer service. D) Optimizing marketing strategies. Show Answer Correct Answer: B) Optimizing production planning. 12. What is the significance of vertices in the feasible region of linear programming? A) They are irrelevant to the solution. B) They represent the highest costs. C) They indicate the lowest output. D) They help determine the optimal solution. Show Answer Correct Answer: D) They help determine the optimal solution. 13. In a standard linear programming problem, the objective function is: A) Always quadratic. B) Always nonlinear. C) Linear and either maximized or minimized. D) Constant. Show Answer Correct Answer: C) Linear and either maximized or minimized. 14. Calculate the determinant of the matrix [[1, 2, 3], [0, 1, 4], [5, 6, 0]]. A) 1. B) 0. C) 10. D) -1. Show Answer Correct Answer: A) 1. 15. Determine if the system of equations 2x + y = 3 and 4x + 2y = 6 is consistent. A) The equations represent parallel lines. B) No, the system is inconsistent. C) The system has no solutions. D) Yes, the system is consistent. Show Answer Correct Answer: D) Yes, the system is consistent. 16. How do you find the maximum value of an objective function? A) Evaluate the objective function at each vertex of the feasible region and identify the highest value. B) Calculate the average of all values in the feasible region. C) Use the derivative of the function to find critical points only. D) Select the highest value from the objective function without considering the feasible region. Show Answer Correct Answer: A) Evaluate the objective function at each vertex of the feasible region and identify the highest value. 17. The feasible region is: A) The area satisfying all constraints. B) The objective function line. C) The set of all possible objective values. D) None of the above. Show Answer Correct Answer: A) The area satisfying all constraints. 18. The feasible region for an LPP is always a ..... polygon. A) CONCAVE. B) CONVEX. C) All the above. D) None of the above. Show Answer Correct Answer: B) CONVEX. 19. In forest management planning, what is the goal of linear programming? A) Minimize species diversity. B) Maximize land area for harvesting. C) Minimize timber yield. D) Maximize timber yield considering constraints. Show Answer Correct Answer: D) Maximize timber yield considering constraints. 20. The type of constraints which specifies maximum capacity of a resource is ..... constraints. A) Greater than or equal. B) Less than. C) Greater than. D) Less than or equal. Show Answer Correct Answer: D) Less than or equal. 21. Define Corner Points A) Limits put on possible outcomes. B) What you are selling. C) A mathematical way of finding the maximum profit with given constraints. D) Vertices where the lines intersect. Show Answer Correct Answer: D) Vertices where the lines intersect. 22. How can the graphical method be used to solve linear programming problems? A) The graphical method can be used to solve linear programming problems by visually representing constraints and the objective function on a graph to find the optimal solution. B) The graphical method involves solving equations algebraically. C) The graphical method cannot be used for linear programming. D) The graphical method only works for non-linear problems. Show Answer Correct Answer: A) The graphical method can be used to solve linear programming problems by visually representing constraints and the objective function on a graph to find the optimal solution. 23. What is the purpose of conducting sensitivity analysis in LP problems? A) To Avoid Optimization. B) To Hide Solutions. C) To Understand the Impact of Changes. D) To Create Confusion. Show Answer Correct Answer: C) To Understand the Impact of Changes. 24. In the graphical method, how many variables can be handled? A) Two. B) Unlimited. C) Three. D) One. Show Answer Correct Answer: A) Two. 25. How can you convert a maximization problem into a minimization problem? A) Change the constraints to be less strict. B) Negate the objective function. C) Add a constant to the objective function. D) Use a different optimization algorithm. Show Answer Correct Answer: B) Negate the objective function. 26. What is a constraint in linear programming? A) A condition that must be satisfied by the solution, typically expressed as a linear inequality or equation. B) A method to optimize the objective function without any limitations. C) A variable that can take any value in the solution space. D) A graphical representation of the feasible region. Show Answer Correct Answer: A) A condition that must be satisfied by the solution, typically expressed as a linear inequality or equation. 27. Which of the following is true about the feasible region? A) It may not exist. B) It is always unbounded. C) It lies outside the origin. D) It is not influenced by constraints. Show Answer Correct Answer: A) It may not exist. 28. The solution space in LPP is called: A) Inequality space. B) Vertex domain. C) Feasible region. D) Range space. Show Answer Correct Answer: C) Feasible region. 29. Given the relation T on the set D = {1, 2, 3} defined by T = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}, is T an equivalence relation? Why or why not? A) T is an equivalence relation because it is symmetric and transitive. B) Yes, T is an equivalence relation because it is reflexive. C) No, T is not an equivalence relation. D) T is an equivalence relation because it contains all pairs of elements. Show Answer Correct Answer: C) No, T is not an equivalence relation. 30. Tentukan x dari $2x+5=11$ A) 3. B) 4. C) 5. D) 2. Show Answer Correct Answer: A) 3. 31. A redundant constraint cannot be removed from the problem without affecting the feasible region.9. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 32. In dual simplex method, the starting solution satisfies the ..... condition A) Feasible. B) Optimal. C) All the above. D) None of the above. Show Answer Correct Answer: B) Optimal. 33. What does the term 'redundancy' refer to in linear programming? A) A constraint that does not affect the feasible region. B) A solution that is not feasible. C) A model with multiple optimal solutions. D) A variable that is not used. Show Answer Correct Answer: A) A constraint that does not affect the feasible region. 34. What does the term 'shadow price' indicate in Linear Programming? A) The maximum profit achievable. B) The value of one additional unit of a resource. C) The minimum cost of production. D) The cost of producing one more unit. Show Answer Correct Answer: B) The value of one additional unit of a resource. 35. For questions 3-6, use the following scenario:Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $ 3 an hour and babysitting pays $ 5 an hour. You need to earn at least $ 60 a week.Let x = # of hours mowingLet y = # of hours babysittingWhich system of inequalities represents the scenario? A) $3x+5y\ge60$ $x+y\le15$. B) $x+y\le60$ $3x+5y\ge15$. C) $x+y\ge60$ $3x+5y\le15$. D) $3x+5y\le60$ $x+y\ge15$. Show Answer Correct Answer: A) $3x+5y\ge60$ $x+y\le15$. 36. What is the role of the graphical method in linear programming? A) It provides a numerical solution to linear programming problems. B) It is a visual approach to solving linear programming problems, allowing for the identification of feasible regions and evaluation of objective functions at vertices. C) It simplifies complex linear equations into single-variable equations. D) It is used to create 3D models of linear programming problems. Show Answer Correct Answer: B) It is a visual approach to solving linear programming problems, allowing for the identification of feasible regions and evaluation of objective functions at vertices. 37. What tool is recommended for teaching graphical solutions to linear inequalities in Session 10.3? A) Microsoft PowerPoint. B) Microsoft Word. C) Microsoft Excel. D) Microsoft Access. Show Answer Correct Answer: C) Microsoft Excel. 38. What is an optimal solution? A) The aim of the problem. B) Values that satisfy all constrains. C) The feasible solution that meets the objective. D) The numbers of each of the things that can be varied. The variables, often called x, y, z etc, will be the 'letters' in the inequalities and the objective function. Show Answer Correct Answer: C) The feasible solution that meets the objective. 39. Which method is used to find the optimal solution in graphical linear programming? A) Simplex method. B) Heuristic method. C) Corner point method. D) Random search method. Show Answer Correct Answer: C) Corner point method. 40. Question 8:What is the significance of the feasible region in solving linear programming problems? A) It is only used for visualization purposes and does not impact the solution. B) It has no significance in solving linear programming problems. C) It represents the set of all possible solutions that satisfy the constraints of the linear programming problem. D) It represents the unattainable solutions of the linear programming problem. Show Answer Correct Answer: C) It represents the set of all possible solutions that satisfy the constraints of the linear programming problem. 41. If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 42. In the graph, this is the intercept when the value of x = 0 A) Y-intercept. B) Vertex. C) First quadrant. D) X-intercept. Show Answer Correct Answer: A) Y-intercept. 43. The assignment problem is a special case of the transportation problem in which one agent is assigned to one, and only one, task. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 44. Find the inverse of the matrix [[1, 2], [3, 4]]. A) [[0, 1], [1, 0]]. B) [[1, 2], [3, 4]]. C) [[-2, 1], [1.5, -0.5]]. D) [[4, 3], [2, 1]]. Show Answer Correct Answer: C) [[-2, 1], [1.5, -0.5]]. 45. All linear programs must seek to maximize some quantity. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 46. The technique that helps to optimize a function subject to constraints by incorporating the constraints into the objective function via multipliers is called: A) Lagrange Multipliers. B) Newton's Method. C) Gradient Descent. D) Interior-Point Method. Show Answer Correct Answer: A) Lagrange Multipliers. 47. First 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: C) Completely understand the managerial problem being faced. 48. What area on a graph shows all possible solutions? A) Solution set. B) Graph boundary. C) Feasible region. D) Intersection points. Show Answer Correct Answer: C) Feasible region. 49. A constraint in LPP represents: A) Maximization target. B) Limitation or restriction. C) Graph axis. D) Objective function. Show Answer Correct Answer: B) Limitation or restriction. 50. Which of the following problems is an example of a blending problem? A) Determining the optimal investment strategy. B) Maximizing profit from product sales. C) Allocating resources for production. D) Finding the best mix of ingredients for a product. Show Answer Correct Answer: D) Finding the best mix of ingredients for a product. 51. Decision variables can never be A) Humans. B) Affirmative. C) Negative. D) Positive. Show Answer Correct Answer: C) Negative. 52. What is the objective function in the given linear programming problem? A) 4x + 3y. B) 5x + 2y. C) 3x + 4y. D) 2x + 5y. Show Answer Correct Answer: A) 4x + 3y. 53. For a minimization problem where z =-3x$_{1}$ + 2x$_{2}$-5x$_{3}$, the corresponding maximization objective function in the standard form will be ..... A) -3x$_{1}$-2x$_{2}$-5x$_{3}$. B) -3x$_{1}$ + 2x$_{2}$-5x$_{3}$. C) 3x$_{1}$ + 2x$_{2}$ + 5x$_{3}$. D) 3x$_{1}$-2x$_{2}$ + 5x$_{3}$. Show Answer Correct Answer: D) 3x$_{1}$-2x$_{2}$ + 5x$_{3}$. 54. Sarah makes at least 18 bags a week. She can't make more than 7 big purses and she can't make more than 10 small purses. Sarah makes $ 30 for each small purse (x) and $ 50 for each big purse (y). What is the objective quantity? A) P= 30x + 50y. B) P = 50x + 30y. C) P= 7x + 10y. D) P= 18x +50y. Show Answer Correct Answer: A) P= 30x + 50y. 55. Consider the following linear programming model.Min 2X1 + 3X2 Subject to:X1 + X2 $\geq$ 4, X1 $\geq$ 2, X1, X2 $\geq$ 0. This linear programming model has: A) Unique optimal solution. B) Infeasible solution. C) Unbounded solution. D) Alternate optimal solution. Show Answer Correct Answer: A) Unique optimal solution. 56. What is the purpose of introducing slack variables in a linear programming model? A) To simplify the objective function. B) To increase the number of variables. C) To decrease the solution space. D) To convert inequalities into equalities. Show Answer Correct Answer: D) To convert inequalities into equalities. 57. What is the balanced transportation model? A) A model where supply equals demand and all constraints are equalities. B) A model where supply is greater than demand. C) A model where demand is greater than supply. D) A model with unbalanced constraints. Show Answer Correct Answer: A) A model where supply equals demand and all constraints are equalities. 58. A decision model has the following input variables:Historical sales data and historical advertising budget. The model is considered to be probabilistic. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: B) FALSE. 59. Can we have more than one optimal solution? A) Optimal solutions are always unique. B) Yes, we can have more than one optimal solution. C) No, there can only be one optimal solution. D) Multiple optimal solutions are not possible in any scenario. Show Answer Correct Answer: B) Yes, we can have more than one optimal solution. 60. Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem? A) Objective Cell values do not converge. B) Solver cannot improve the current solution. All constraints are satisfied. C) Solver could not find a feasible solution. D) Solver could not find a bounded solution. Show Answer Correct Answer: A) Objective Cell values do not converge. ← 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 8 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books