This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 5 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If the Objective quantity is:30x + 50yAnd the corner that maximizes profit is:(0, 6)What is the profit? A) 400. B) 300. C) 280. D) 240. Show Answer Correct Answer: B) 300. 2. What are the limitations of linear programming? A) Unknown parameters. B) Discrete variables. C) Assumption of non-linearity. D) Assumption of linearity, known parameters, continuous variables, independence, single objective function. Show Answer Correct Answer: D) Assumption of linearity, known parameters, continuous variables, independence, single objective function. 3. What happens in a Linear Programming problem if the solution is unbounded? A) The solution is optimal. B) The profit can increase indefinitely. C) The solution is infeasible. D) The constraints are contradictory. Show Answer Correct Answer: B) The profit can increase indefinitely. 4. What is the significance of corner points in linear programming? A) Corner points only represent infeasible solutions. B) Corner points are significant as they are potential optimal solutions in linear programming. C) Corner points are used to determine the feasibility of constraints. D) Corner points are irrelevant in linear programming. Show Answer Correct Answer: B) Corner points are significant as they are potential optimal solutions in linear programming. 5. For a minimization problem, the solution is considered to be unbounded if the value may be made infinitely small.10. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 6. How can linear programming be used to optimize portfolio selection in finance? A) By maximizing the return or minimizing the risk of a portfolio subject to certain constraints. B) By finding the average return of all possible investment portfolios. C) By eliminating all risk to find the best possible investment outcome. D) By assuming all investment returns are independent of each other. Show Answer Correct Answer: A) By maximizing the return or minimizing the risk of a portfolio subject to certain constraints. 7. What is the value of the objective function at the point (3, 2)? A) 12. B) 18. C) 24. D) 15. Show Answer Correct Answer: B) 18. 8. Graph and identify a possible solution. Identify the slope and y-intercept. Use graph paper. Label each inequality and shade.y$\geq$2x+3y$\geq$1/3x-2 A) (-3, 3). B) (-4, -4). C) (3, 3). D) (-1, -1). Show Answer Correct Answer: A) (-3, 3). 9. How do you graph a linear inequality in two dimensions? A) Graph the corresponding line, then shade the appropriate region based on the inequality. B) Shade the entire graph without considering the inequality. C) Only plot the points that satisfy the inequality without drawing the line. D) Draw a circle around the line and leave it blank. Show Answer Correct Answer: A) Graph the corresponding line, then shade the appropriate region based on the inequality. 10. If all the values of the input variables in a decision model are random in nature, then the model is considered to be probabilistic. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 11. How do you determine if a point lies within the feasible region? A) A point is always feasible if it is an integer. B) A point lies within the feasible region if it is outside the constraints. C) A point lies within the feasible region if it satisfies all the constraints defining that region. D) A point is feasible if it meets at least one constraint. Show Answer Correct Answer: C) A point lies within the feasible region if it satisfies all the constraints defining that region. 12. A basic feasible solution to a (m x n) transportation problem is said to be a ..... solution ifit contains exactly m + n-1 non negative allocations in independent positions A) Infeasible. B) Basic feasible. C) Non degenerate basic feasible. D) Feasible. Show Answer Correct Answer: C) Non degenerate basic feasible. 13. Formulate a linear programming problem for a diet plan that meets nutritional requirements. A) Focus solely on taste without considering cost or nutrition. B) Minimize variety to reduce meal preparation time. C) Maximize calories while ignoring nutritional needs. D) Minimize cost subject to nutritional constraints for a balanced diet. Show Answer Correct Answer: D) Minimize cost subject to nutritional constraints for a balanced diet. 14. Provide an example of a real-world application where linear programming can be effectively used. A) Supply chain management. B) Weather forecasting. C) Social media marketing. D) Personal finance management. Show Answer Correct Answer: A) Supply chain management. 15. Which of the following is a property of all linear programming problems? A) We can choose from alternate courses of action. B) Minimization of some objective. C) A computer program. D) Usage of graphs in the solution. E) Usage of linear and nonlinear equations and inequalities. Show Answer Correct Answer: A) We can choose from alternate courses of action. 16. What is the defining characteristic of a Non-Linear Programming (NLP) problem? A) Both the objective function and all constraints must be linear. B) Only the constraints must be non-linear. C) The objective function or the constraints (or both) are non-linear. D) The problem must only involve discrete variables. Show Answer Correct Answer: C) The objective function or the constraints (or both) are non-linear. 17. The imposition of an integer restriction is necessary for models where A) Nonnegativity constraints are needed. B) The decision variables cannot take fractional values. C) Variables can take negative values. D) Possible values of variables are restricted to particular intervals. Show Answer Correct Answer: B) The decision variables cannot take fractional values. 18. Which of the following statements about infeasible problems is best? A) All of the possible solutions violate at least one constraint. B) All of the possible solutions violate all of the constraints. C) At least one of the possible solutions violates all of the constraints. D) At least one of the possible solutions violates at least one of the constraints. Show Answer Correct Answer: A) All of the possible solutions violate at least one constraint. 19. The constraint x1-x2 = 0 implies that if project 1 is selected, project 2 cannot be. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 20. Assumer there is a total of n variables and m constraints in an LP model. Each variable can be either ..... variable or ..... variable. A) Bad; good. B) Feasible; non-feasible. C) Basic; non-basic. D) Optimal; non-optimal. Show Answer Correct Answer: C) Basic; non-basic. 21. What does the shaded region in a system of inequalities represent? A) The average of all lines. B) The maximum value of the function. C) The intersection of all solutions. D) The midpoint of the graph. Show Answer Correct Answer: C) The intersection of all solutions. 22. To find the optimal solution for maximum cases, all entries in the objective row of the final tableau are ..... A) Positive. B) Negative. C) All the above. D) None of the above. Show Answer Correct Answer: A) Positive. 23. LPP is widely used in: A) Resource allocation. B) Weather forecasting. C) Painting. D) None of the above. Show Answer Correct Answer: A) Resource allocation. 24. What is the role of slack variables in linear programming? A) Slack variables are introduced to minimize the number of constraints in linear programming. B) Slack variables convert inequality constraints into equality constraints in linear programming. C) Slack variables are used to maximize the objective function in linear programming. D) Slack variables are only applicable to integer programming, not linear programming. Show Answer Correct Answer: B) Slack variables convert inequality constraints into equality constraints in linear programming. 25. If the feasible region for a LPP is unbounded, maximum or minimum of theobjective function Z = ax + by may or may not exist. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 26. The region that satisfies all the constraints in a linear programming problem is called: A) Optimal solution. B) Feasible region. C) Objective function. D) Decision region. Show Answer Correct Answer: B) Feasible region. 27. What is the outcome of completing Unit-10? A) Balancing Competing Objectives. B) Understanding Real-World Problems. C) Solving Cryptography Puzzles. D) Analyzing Historical Events. Show Answer Correct Answer: A) Balancing Competing Objectives. 28. Identify the feasible region for the inequalities x >= 0, y >= 0, and x + 2y <= 8. A) The feasible region is a rectangle with vertices at (0, 0), (0, 8), (8, 8), and (8, 0). B) The feasible region is the triangle with vertices at (0, 0), (0, 4), and (8, 0). C) The feasible region is a line passing through (0, 0) and (8, 8). D) The feasible region is a circle with center at (4, 4) and radius 4. Show Answer Correct Answer: B) The feasible region is the triangle with vertices at (0, 0), (0, 4), and (8, 0). 29. How do you identify the feasible region in a graphical method? A) The feasible region is the entire graph area. B) The feasible region is the area on the graph where all constraints are satisfied. C) The feasible region is only the boundary lines of the constraints. D) The feasible region is where no constraints are met. Show Answer Correct Answer: B) The feasible region is the area on the graph where all constraints are satisfied. 30. When optimizing harvesting planning and scheduling using LP, what is the objective? A) Minimize harvesting costs. B) Maximize tree growth rates. C) Ignore market demand. D) Increase operational constraints. Show Answer Correct Answer: A) Minimize harvesting costs. 31. What are the constraints in a linear programming problem? A) Constraints are only applicable to integer programming problems. B) Constraints are always quadratic equations that maximize profit. C) Constraints in a linear programming problem are linear inequalities or equations that represent limitations on resources. D) Constraints are irrelevant to the solution of linear programming problems. Show Answer Correct Answer: C) Constraints in a linear programming problem are linear inequalities or equations that represent limitations on resources. 32. What is the main purpose of linear programming? A) Creating graphs. B) Writing computer code. C) Maximizing or minimizing a particular outcome. D) Solving complex equations. Show Answer Correct Answer: C) Maximizing or minimizing a particular outcome. 33. How can graphical solutions to linear inequalities be used in real-life scenarios? A) Designing architectural structures. B) Optimizing transportation routes. C) Creating artistic compositions. D) Predicting weather patterns. Show Answer Correct Answer: B) Optimizing transportation routes. 34. What is the objective of a business in linear programming? A) To maximize profit. B) To minimize cost. C) To balance supply and demand. D) To find the optimal solution. Show Answer Correct Answer: A) To maximize profit. 35. Which field does not use linear programming for decision-making? A) Music. B) Military planning. C) Business. D) Economics. Show Answer Correct Answer: A) Music. 36. Find the inverse of the matrix [[4, 7], [2, 6]]. A) [[0, 1], [1, 0]]. B) [[4, 2], [6, 7]]. C) [[1, 2], [3, 4]]. D) [[0.6, -0.7], [-0.2, 0.4]]. Show Answer Correct Answer: D) [[0.6, -0.7], [-0.2, 0.4]]. 37. What is the slope? y= 1/2x +-8 A) -8. B) 1/2. C) 1/2x. D) -1/2. Show Answer Correct Answer: B) 1/2. 38. In dual simplex, we first determine ..... Variable and ..... variable. A) Basic, Infeasible. B) Leaving, Feasible. C) Leaving, entering. D) Entering, leaving. Show Answer Correct Answer: C) Leaving, entering. 39. In a linear programming problem, what's another term for the "corners" of the feasible region? A) Vertices. B) Objectives. C) Slope. D) Inequalities. Show Answer Correct Answer: A) Vertices. 40. A numerical coefficients and constants used in the objective function and constraints. A) CONSTRAINTS. B) PARAMETERS. C) OBJECTIVE FUNCTION. D) DECISION VARIABLES. Show Answer Correct Answer: B) PARAMETERS. 41. The feasible region in a linear programming problem is always: A) Convex. B) Circular. C) Unbounded. D) Concave. Show Answer Correct Answer: A) Convex. 42. In Phase 1, a cost ..... is assigned to all variables except artificial variable A) M. B) -1. C) 0. D) 1. Show Answer Correct Answer: C) 0. 43. How do you graph multiple linear inequalities on the same coordinate plane? A) To graph multiple linear inequalities, graph each inequality's boundary line, shade the appropriate region, and repeat for all inequalities. B) Only graph the first inequality and ignore the rest. C) Use only dotted lines for all inequalities regardless of type. D) Shade all regions without considering the boundaries. Show Answer Correct Answer: A) To graph multiple linear inequalities, graph each inequality's boundary line, shade the appropriate region, and repeat for all inequalities. 44. Explain how to find the optimal solution using graphical methods. A) Select any point within the feasible region. B) Draw random lines on the graph. C) Plot feasible region, identify corner points, calculate objective function at each corner point, choose highest (or lowest) value. D) Use trial and error method to find the solution. Show Answer Correct Answer: C) Plot feasible region, identify corner points, calculate objective function at each corner point, choose highest (or lowest) value. 45. The K.V. 1 Bathinda Club plans to grow trees as a project. There is a 1200 square foot plot of land available at their school to grow balsam fir and Douglas fir trees. There are only 576 pounds of fertilizer available.The profit for each balsam fir tree is $ 15 and $ 18 for each Douglas fir tree.Which of the following is an Objective Function that relates maximum profit? A) P = 576x + 1200y. B) P = 1200x + 576y. C) P = 15x + 18y. D) P = x + y. Show Answer Correct Answer: C) P = 15x + 18y. 46. What is the relationship between constraints and the feasible region? A) Constraints define the boundaries of the feasible region; the area where all constraints overlap represents the feasible solutions. B) Constraints are irrelevant to the feasible region and do not affect the solutions. C) The feasible region is always larger than the constraints defined. D) Constraints only apply to linear equations and do not relate to the feasible region. Show Answer Correct Answer: A) Constraints define the boundaries of the feasible region; the area where all constraints overlap represents the feasible solutions. 47. What is the inequality for SEWING TIME? A) 6x + 3y < 24. B) 2x + 3y < 24. C) 2x + 3y < 36. D) 6x + 3y < 36. Show Answer Correct Answer: D) 6x + 3y < 36. 48. What is the significance of the corner points in the feasible region? A) The corner points are always the worst solutions in the feasible region. B) The corner points only indicate the boundaries of the region. C) The corner points are irrelevant to the feasible region. D) The corner points are significant as they represent potential optimal solutions in the feasible region. Show Answer Correct Answer: D) The corner points are significant as they represent potential optimal solutions in the feasible region. 49. What is the benefit of using Microsoft Excel for solving linear programming problems? A) Perform statistical analysis only. B) Efficiently analyze complex problems and make data-driven decisions. C) Limited functionality compared to other tools. D) Create artistic graphs and charts. Show Answer Correct Answer: B) Efficiently analyze complex problems and make data-driven decisions. 50. What is the transportation problem? A) Allocating items from sources to destinations at a minimum cost. B) Maximizing profit in transportation. C) Minimizing cost in transportation. D) Balancing supply and demand. Show Answer Correct Answer: A) Allocating items from sources to destinations at a minimum cost. 51. What is the y-intercept of the equation?y =-2x + 3 A) -3. B) -2. C) 3. D) 1. Show Answer Correct Answer: C) 3. 52. How can LP be used in healthcare administration? A) Allocating resources in hospitals. B) Managing investment portfolios. C) Planning crop rotations. D) Optimizing transportation routes. Show Answer Correct Answer: A) Allocating resources in hospitals. 53. Explain the concept of constraints in linear programming. A) Constraints are suggestions in linear programming that can be ignored. B) Constraints are not necessary for solving linear programming problems. C) Constraints in linear programming are limitations or restrictions on decision variables that must be satisfied to optimize the objective function. D) Constraints are only applicable to the objective function in linear programming. Show Answer Correct Answer: C) Constraints in linear programming are limitations or restrictions on decision variables that must be satisfied to optimize the objective function. 54. What is the optimal solution in LP typically found at? A) At one of the corner points of the feasible region. B) At random points. C) At the center of the feasible region. D) At the edges of the feasible region. Show Answer Correct Answer: A) At one of the corner points of the feasible region. 55. How can graphical solutions methods be applied in manufacturing companies? A) Optimizing production planning. B) Managing customer service. C) Handling financial transactions. D) Analyzing market trends. Show Answer Correct Answer: A) Optimizing production planning. 56. A major challenge in solving real-world NLP problems is that non-convex functions are common. Why are these functions particularly difficult to handle? A) They only apply to discrete variables. B) They cannot be solved by any known algorithm. C) Local optimization techniques may not find the global optimum. D) They do not have any constraints. Show Answer Correct Answer: C) Local optimization techniques may not find the global optimum. 57. Lexie is making apple cobblers and apple pies for a bake sale. A cobbler needs 6 cups of apples and a pie needs 2 cups of apples. She also needs to use 4 cups of flour for a cobbler and 2 cups of flour for a pie. Lexie has 18 cups of apples and 16 cups of flour. x= # of cobblers and y is # of pieswrite the inequality for the amount of apples A) $2x+4y\le16$. B) $6x+2y\le18$. C) $2x+6y\le18$. D) $4x+2y\le16$. Show Answer Correct Answer: B) $6x+2y\le18$. 58. Solve using elimination:6x-4y = 28 2x + 2y = 6, A) X = 2, y = 1. B) X = 4, y =-1. C) X = 1, y = 2. D) X =-4, y = 1. Show Answer Correct Answer: B) X = 4, y =-1. 59. What is the main focus of Session 10.2? A) Teaching Calculus. B) Teaching Linear Programming. C) Teaching Geometry. D) Teaching Algebra. Show Answer Correct Answer: B) Teaching Linear Programming. 60. What is linear programming? A) A mathematical technique to solve allocation of resources. B) A model that represents a firm's decision given an objective and constraints. C) A method to maximize profit or minimize cost. D) All of the above. Show Answer Correct Answer: D) All of the above. ← 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 6Class 12 Mathematics Chapter 12 Linear Programming Quiz 7Class 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