This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 7 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 7 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. It is the application of quantitative scientific methods, techniques and tools to arrive at optimum solutions to complex organizational activities. A) Linear programming. B) Modelling. C) Operations research. D) None of the above. Show Answer Correct Answer: C) Operations research. 2. What is the main focus of Unit-10 in the training module? A) Teaching Linear Programming. B) Teaching Geometry. C) Teaching Algebra. D) Teaching Calculus. Show Answer Correct Answer: A) Teaching Linear Programming. 3. What is the purpose of scenario analysis in LP problems? A) To Limit Solutions. B) To Avoid Decision Making. C) To Explore Different Scenarios. D) To Create Chaos. Show Answer Correct Answer: C) To Explore Different Scenarios. 4. Calculate the determinant of the matrix [[2, 5], [3, 7]]. A) 10. B) -1. C) 5. D) 0. Show Answer Correct Answer: B) -1. 5. How can teachers identify the feasible region in linear inequalities? A) By Guessing Randomly. B) By Memorizing Formulas. C) By Solving Quadratic Equations. D) By Graphing the Constraints. Show Answer Correct Answer: D) By Graphing the Constraints. 6. The solution which do not satisfy all the constraints of linear programming problem is called A) Infeasible solution. B) Degenerate solution. C) Optimal feasible solution. D) None of above. Show Answer Correct Answer: A) Infeasible solution. 7. Question 10:How does the feasible region help in finding the optimal solution in linear programming? A) By identifying the area where all constraints are satisfied, and the objective function can be optimized. B) By drawing a line through the feasible region. C) By randomly selecting a point within the feasible region. D) By ignoring all constraints and focusing only on the objective function. Show Answer Correct Answer: A) By identifying the area where all constraints are satisfied, and the objective function can be optimized. 8. Linear programming is used to: A) Solve nonlinear equations. B) Compute matrix inverses. C) Solve differential equations. D) Maximize or minimize a linear objective function. Show Answer Correct Answer: D) Maximize or minimize a linear objective function. 9. Shreya owns a car and a moped. She has at most 12 litres of petrol to be used between the car and the moped. The car's tank holds at most 10 litres and the moped's 3 litres. The mileage for the car is 20 km/l and for the moped is 100 km/l. What are the variables you need to define? A) X is car, y is moped. B) X is petrol, y is moped. C) X is car, y is mileage. D) X is petrol, y is mileage. Show Answer Correct Answer: A) X is car, y is moped. 10. The change in the optimal objective function value per unit increase in the right-hand side of a constraint is given by the A) Allowable increase. B) Shadow price. C) Objective function coefficient. D) Restrictive cost. Show Answer Correct Answer: B) Shadow price. 11. What is the feasible region in linear programming? A) The region where all constraints are satisfied simultaneously. B) The region with the most constraints. C) The region with the highest costs. D) The region with the lowest output. Show Answer Correct Answer: A) The region where all constraints are satisfied simultaneously. 12. What does the objective function represent in a linear programming problem? A) The objective function defines the constraints of the problem. B) The objective function is used to calculate the feasible region. C) The objective function represents the goal of optimization in a linear programming problem. D) The objective function represents the variables in the problem. Show Answer Correct Answer: C) The objective function represents the goal of optimization in a linear programming problem. 13. Dennis mowed his next door neighbor's lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $ 6.60. Which system of equations could be used to find the exact number of dimes and nickels? A) D + n = 6.60.10d + .05n = 80. B) D + n = 80.05d + .10n = 6.60. C) D + n = 80d + n = 6.60. D) D + n = 80.10d + .05n = 6.60. Show Answer Correct Answer: D) D + n = 80.10d + .05n = 6.60. 14. Solve the system by substitution. 5x + 4y=-14 y =-7x-15 A) (-2, -1). B) (1, -2). C) (-1, -2). D) (-2, 1). Show Answer Correct Answer: A) (-2, -1). 15. How do you graph a linear inequality? A) Only plot the y-intercept. B) Connect the points with a dashed line. C) Graph the corresponding linear equation, then shade the appropriate side based on a test point. D) Draw a circle around the equation. Show Answer Correct Answer: C) Graph the corresponding linear equation, then shade the appropriate side based on a test point. 16. What is the purpose of the graphic solution method in linear programming? A) To determine the optimal solution for problems with two decision variables. B) To identify the entry variable. C) To improve the initial feasible solution. D) To convert inequalities into equations. Show Answer Correct Answer: A) To determine the optimal solution for problems with two decision variables. 17. An inequality using > or < has a ..... line. A) Solid. B) Dashed. C) All the above. D) None of the above. Show Answer Correct Answer: B) Dashed. 18. What type of functions would be produced when examining profits and costs? A) Inequalities. B) Equations. C) Expressions. D) None of the above. Show Answer Correct Answer: A) Inequalities. 19. Identify the feasible region for the inequalities x >= 0, y >= 0, and 2x + 3y <= 9. A) The feasible region is a rectangle with vertices (0, 0), (0, 9), (9, 0), and (9, 9). B) The feasible region is the triangle with vertices (0, 0), (0, 3), and (4.5, 0). C) The feasible region is a line segment from (0, 0) to (9, 0). D) The feasible region is a circle with center (0, 0) and radius 3. Show Answer Correct Answer: B) The feasible region is the triangle with vertices (0, 0), (0, 3), and (4.5, 0). 20. If the feasible region is empty, what does it mean? A) No solution exists. B) Constraints are redundant. C) Objective function is zero. D) Infinite solutions exist. Show Answer Correct Answer: A) No solution exists. 21. Given the relation S on the set C = {1, 2, 3, 4} defined by S = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1)}, is S an equivalence relation? Why or why not? A) No, S is not an equivalence relation because it is not reflexive. B) Yes, S is an equivalence relation because it is reflexive. C) No, S is not an equivalence relation because it is not transitive. D) Yes, S is an equivalence relation because it is symmetric. Show Answer Correct Answer: C) No, S is not an equivalence relation because it is not transitive. 22. It requires that each variables to be greater than or equal to zero A) Maximization. B) Minimization. C) Inequality. D) Non-negativity constraints. Show Answer Correct Answer: D) Non-negativity constraints. 23. 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. Which of the following points is NOT a vertex of the shaded region? A) (0, 3). B) (0, 0). C) (10, 2). D) (6, 6). Show Answer Correct Answer: D) (6, 6). 24. In linear programming, what does the objective function usually represent? A) The shape of the graph. B) The axis labels. C) The cost or profit to be optimized. D) The type of inequality. Show Answer Correct Answer: C) The cost or profit to be optimized. 25. An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.5. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 26. If the optimal solution to the LP Relaxation problem is an integer, it is the optimal solution to the integer linear program. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 27. Michael is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $ 1.50 each and sodas cost $ 0.50 each. At the end of the game, Michael wants to make more than $ 78.50 and sell less than 87 items. Which system of equations represents this situation? A) 1.5x+0.5y$\geq$78.51.5x+0.5y<87. B) X+y$\geq$78.5x+y<87. C) 1.5x+0.5y>78.5x+y<87. D) 1.5x+0.5y$\geq$78.5x+y<87. Show Answer Correct Answer: C) 1.5x+0.5y>78.5x+y<87. 28. How can you represent constraints graphically in a linear programming problem? A) Plot each constraint as a line, shade the feasible region, and identify the optimal solution at the vertices. B) Use only numerical values without graphical representation. C) Shade the entire graph without identifying regions. D) Draw only the objective function line. Show Answer Correct Answer: A) Plot each constraint as a line, shade the feasible region, and identify the optimal solution at the vertices. 29. The measurable input quantity that is inherent in the problem A) Variables. B) Parameter. C) Constraints. D) Decision variables. Show Answer Correct Answer: B) Parameter. 30. In an LP, best corner point feasible solution must be an optimal solution. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 31. A Transportation problem is a special case of linear programming problem A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 32. What is the primary purpose of using quantitative techniques in management decision making? A) To rely solely on intuition. B) To ignore data analysis. C) To provide a systematic and objective approach to analyzing data and making informed decisions. D) To complicate decision-making processes. Show Answer Correct Answer: C) To provide a systematic and objective approach to analyzing data and making informed decisions. 33. Where can graphical solutions methods be applied in financial analysis? A) Planning crop rotations. B) Optimizing transportation routes. C) Allocating resources in hospitals. D) Managing investment portfolios. Show Answer Correct Answer: D) Managing investment portfolios. 34. Calculate the determinant of the matrix [[2, 3], [1, 4]]. A) 8. B) 7. C) 6. D) 5. Show Answer Correct Answer: D) 5. 35. A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y? A) Y=80x+15. B) Y=15x+80. C) Y=x+15. D) Y=15x. Show Answer Correct Answer: B) Y=15x+80. 36. It refers to the activities carried out within the organization related to attaining goals and objectives A) Planning. B) Operations. C) Scientific method. D) Allocation of resources. Show Answer Correct Answer: B) Operations. 37. What is the difference between bounded and unbounded feasible regions? A) Bounded regions can extend infinitely in all directions. B) Bounded regions are finite and enclosed, while unbounded regions extend infinitely in at least one direction. C) Unbounded regions are always enclosed and finite. D) Bounded regions are infinite and unconfined. Show Answer Correct Answer: B) Bounded regions are finite and enclosed, while unbounded regions extend infinitely in at least one direction. 38. How are constraints represented graphically in the graphical method? A) By adding more variables to the graph. B) By drawing lines or boundaries. C) By using circles instead of lines. D) By shading the feasible region. Show Answer Correct Answer: B) By drawing lines or boundaries. 39. Calculate the determinant of the matrix [[1, 0, 2], [0, 1, 3], [0, 0, 1]]. A) 0. B) -1. C) 1. D) 2. Show Answer Correct Answer: C) 1. 40. Pelajar S diwakili x dan pelajar R diwakili y.I) Jumlah bilangan pelajar tidak lebih daripada 90 orang.II) Bilangan pelajar S tidak lebih daripada dua kali bilangan pelajar R.III) Bilangan pelajar R mesti melebihi bilangan pelajar Ssebanyak selebih-lebihnya 10 orang. A) $x+y\le90$ $y\le2x$ $y\le10+x$. B) $x+y\le90$ $y\ge2x$ $y-x\le10$. C) $y\le90-x$ $x\le2y$ $y-x\ge10$. D) $x+y\le90$ $x\le2y$ $y-x\le10$. Show Answer Correct Answer: D) $x+y\le90$ $x\le2y$ $y-x\le10$. 41. What is the main benefit of using Microsoft Excel for LP problems? A) To confuse students. B) To optimize decision-making. C) To avoid calculations. D) To create more problems. Show Answer Correct Answer: B) To optimize decision-making. 42. Question 7:How do you determine if a point is within the feasible region in linear programming? A) Substitute the coordinates of the point into the constraints of the problem and check if they are satisfied. B) Check if the point is located on the x-axis. C) Count the number of variables in the linear programming problem. D) Use the Pythagorean theorem to calculate the distance from the point to the origin. Show Answer Correct Answer: A) Substitute the coordinates of the point into the constraints of the problem and check if they are satisfied. 43. The closed plain region obtained by the intersection of planes determined by a set of the constraints in the LP problem A) Objective Function. B) Feasible Region. C) Decsriptive Analysis. D) Corner Point Method. Show Answer Correct Answer: B) Feasible Region. 44. Data processed to reveal meaning A) DATABASE. B) DATA WAREHOUSE. C) INFORMATION. D) DATA. Show Answer Correct Answer: C) INFORMATION. 45. What is a feasible solution? A) A solution that violates constraints. B) A solution that meets all constraints. C) A solution that is impossible. D) A solution that is not optimal. Show Answer Correct Answer: B) A solution that meets all constraints. 46. Maximum value of the objective function Z = ax + by in a LPP always occurs atonly one corner point of the feasible region. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: B) FALSE. 47. What is the main benefit of linear programming? A) Maximizing profit without limitations. B) Ignoring constraints. C) Creating random outcomes. D) Optimizing outcomes in various scenarios. Show Answer Correct Answer: D) Optimizing outcomes in various scenarios. 48. What is the objective of sensitivity analysis in linear programming? A) To understand how changes in parameters impact the optimal solution. B) To ignore constraints. C) To minimize the decision variables. D) To maximize the objective function. Show Answer Correct Answer: A) To understand how changes in parameters impact the optimal solution. 49. Why is it important to connect classroom learning to everyday scenarios in linear programming? A) To make learning more difficult. B) To confuse students with irrelevant examples. C) To help students appreciate the value of mathematics in solving real-world problems. D) To discourage students from studying mathematics. Show Answer Correct Answer: C) To help students appreciate the value of mathematics in solving real-world problems. 50. How do you determine the maximum or minimum value of the objective function? A) Assume the function is always increasing or decreasing. B) Use only trial and error to guess values. C) Use calculus, linear programming, or graphical methods to find critical points and evaluate the objective function. D) Ignore constraints and focus on random values. Show Answer Correct Answer: C) Use calculus, linear programming, or graphical methods to find critical points and evaluate the objective function. 51. Which of the following is true of rounding the optimized solution of a linear program to an integer? A) It does not affect the value of the objective function. B) It always produces the most optimal integer solution. C) It always produces a feasible solution. D) It may or may not be feasible. Show Answer Correct Answer: D) It may or may not be feasible. 52. Which ordered pair will maximize P = 3x + y with the following constraints:$x+y\\le300$ $y\\ge100$ $x\\le150$ A) X = 100, y 150. B) X = 150, y = 150. C) X = 0, y = 300. D) X = 150, y = 100. Show Answer Correct Answer: B) X = 150, y = 150. 53. Which of the following is a common application of Linear Programming? A) Inventory management. B) Scheduling tasks. C) Market analysis. D) Quality control. Show Answer Correct Answer: B) Scheduling tasks. 54. Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which one of these is a valid solution? A) (2, 8). B) (3, 2). C) (5, 1). D) (1, 4). Show Answer Correct Answer: C) (5, 1). 55. What is the purpose of the objective function in LP? A) To minimize or maximize a quantity. B) To make the problem harder. C) To confuse students. D) To add unnecessary complexity. Show Answer Correct Answer: A) To minimize or maximize a quantity. 56. Explain how to determine if a solution is optimal in a linear programming problem. A) A solution is optimal if it has the highest number of variables. B) A solution is optimal if it is the first one found during the process. C) A solution is optimal if it meets only one constraint. D) A solution is optimal if it satisfies all constraints and no better objective value can be achieved. Show Answer Correct Answer: D) A solution is optimal if it satisfies all constraints and no better objective value can be achieved. 57. Graph the inequality x-2y < 4 and identify the feasible region. A) The feasible region is the area on the dashed line y = (1/2)x-2. B) The feasible region is the area below the dashed line y = (1/2)x-2. C) The feasible region is the area above the dashed line y = (1/2)x-2. D) The feasible region is the area to the left of the dashed line y = (1/2)x-2. Show Answer Correct Answer: C) The feasible region is the area above the dashed line y = (1/2)x-2. 58. Solve. |-x-10| + 4 <-8 A) No solution. B) X > 2 or x <-22. C) -22 < x < 2. D) All real numbers. Show Answer Correct Answer: A) No solution. 59. A constraint that does NOT affect the feasible region of the solution is a15. A. nonnegativity constraint.B. redundant constraint.C. standard constraint.D. slack constraint. A) B. B) D. C) A. D) C. Show Answer Correct Answer: A) B. 60. A special case when the objection function can be made infinitely large without violating any of the constraints A) Infeasibility. B) Alternate solutions. C) Redundancy. D) Unboundedness. Show Answer Correct Answer: D) Unboundedness. ← 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 8Class 12 Mathematics Chapter 12 Linear Programming Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books