This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 3 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. 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) One solution. B) No solutions. C) Infinitely many solutions. D) Two solutions. Show Answer Correct Answer: C) Infinitely many solutions. 2. What do we call the things we want to find in a problem? A) Parameters. B) Variables. C) Constants. D) Equations. Show Answer Correct Answer: B) Variables. 3. ..... are the restrictions or limitation imposed on the linear programming problem. A) Cost. B) Variables. C) Constraints. D) Profit. Show Answer Correct Answer: C) Constraints. 4. In the Beaver Creek example, what is the profit per unit for a bowl? A) $ 20. B) $ 40. C) $ 50. D) $ 30. Show Answer Correct Answer: B) $ 40. 5. 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. 6. Determine if the system of equations 2x + 3y = 5 and 4x + 6y = 10 is consistent. A) The system is inconsistent. B) The system has no solutions. C) The system has infinitely many solutions. D) The system is consistent. Show Answer Correct Answer: D) The system is consistent. 7. 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. 8. Solve using elimination:x-y=112x+y=19 A) (10, -1). B) (-1, 10). C) (3, -4). D) (6, 7). Show Answer Correct Answer: A) (10, -1). 9. In linear programming, what are decision variables? A) Variables that can take any value. B) Variables that are always negative. C) Variables that are only integers. D) Variables that are non-negative. Show Answer Correct Answer: D) Variables that are non-negative. 10. What is the primary focus of Session 10.4? A) Teaching Linear Programming. B) Teaching Statistics. C) Teaching Calculus. D) Teaching Algebra. Show Answer Correct Answer: A) Teaching Linear Programming. 11. 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. 12. 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. 13. 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. 14. 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. 15. A controllable input for a linear programming model is known as a A) Decision variable. B) Dummy variable. C) Parameter. D) Constraint. Show Answer Correct Answer: A) Decision variable. 16. The number of non basic variables in the balanced transportation problem with 3 rowsand 5 columns is ..... A) 15. B) 7. C) 8. D) 9. Show Answer Correct Answer: B) 7. 17. Which method is used to find the optimal solution in a Linear Programming problem with two variables? A) Dynamic Programming. B) Integer Programming. C) Graphical Method. D) Simplex Method. Show Answer Correct Answer: C) Graphical Method. 18. What is the goal of linear programming? A) To complicate decision-making. B) To minimize profit. C) To ignore constraints. D) To optimize outcomes within certain constraints. Show Answer Correct Answer: D) To optimize outcomes within certain constraints. 19. At which point does the minimum value of the objective function occur? A) (0, 5). B) (3, 2). C) (6, 0). D) (5, 5). Show Answer Correct Answer: A) (0, 5). 20. Solve for x and y (use substitution)3x + 2y = 167x + y = 19 A) (-2, 5). B) (-2, -5). C) (2, -5). D) (2, 5). Show Answer Correct Answer: D) (2, 5). 21. What is the graphical representation of a linear programming problem called? A) Feasible region. B) Objective function. C) Constraint line. D) Corner point. Show Answer Correct Answer: A) Feasible region. 22. It measures the quantity that is subject to change. A) Decision variables. B) Parameter. C) Constraints. D) Variables. Show Answer Correct Answer: D) Variables. 23. What is the purpose of the objective function in Linear Programming? A) To define the constraints. B) To calculate the shadow price. C) To represent the decision variables. D) To express the goal of the optimization. Show Answer Correct Answer: D) To express the goal of the optimization. 24. According to the text, what is a key limitation or consideration when solving NLP problems? A) The solutions are always easy to interpret. B) The problems are less complex than linear problems. C) Solutions are sensitive to initial conditions and may converge to local optima. D) They can only be used for small-scale problems. Show Answer Correct Answer: C) Solutions are sensitive to initial conditions and may converge to local optima. 25. How do you graph constraints in linear programming? A) Convert inequalities into equations, plot the lines on a graph, and shade the appropriate regions to represent the constraints. B) Only plot the lines without shading any regions. C) Use only the equations without converting inequalities. D) Shade all regions on the graph regardless of the constraints. Show Answer Correct Answer: A) Convert inequalities into equations, plot the lines on a graph, and shade the appropriate regions to represent the constraints. ← PreviousNext →Related QuizzesClass 12 Mathematics Chapter 12 Linear Programming Quiz 1Class 12 Mathematics Chapter 12 Linear Programming Quiz 2Class 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 8Class 12 Mathematics Chapter 12 Linear Programming Quiz 9Class 12 Mathematics Chapter 12 Linear Programming Quiz 10Class 12 Mathematics Chapter 12 Linear Programming Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books