This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The number of non basic variables in the balanced transportation problem with 3 rowsand 5 columns is ..... A) 7. B) 8. C) 9. D) 15. Show Answer Correct Answer: A) 7. 2. Which method is used to find the optimal solution in a Linear Programming problem with two variables? A) Integer Programming. B) Graphical Method. C) Dynamic Programming. D) Simplex Method. Show Answer Correct Answer: B) Graphical Method. 3. What is the goal of linear programming? A) To optimize outcomes within certain constraints. B) To complicate decision-making. C) To minimize profit. D) To ignore constraints. Show Answer Correct Answer: A) To optimize outcomes within certain constraints. 4. 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). 5. 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). 6. What is the graphical representation of a linear programming problem called? A) Corner point. B) Constraint line. C) Feasible region. D) Objective function. Show Answer Correct Answer: C) Feasible region. 7. It measures the quantity that is subject to change. A) Constraints. B) Parameter. C) Decision variables. D) Variables. Show Answer Correct Answer: D) Variables. 8. What is the purpose of the objective function in Linear Programming? A) To express the goal of the optimization. B) To define the constraints. C) To calculate the shadow price. D) To represent the decision variables. Show Answer Correct Answer: A) To express the goal of the optimization. 9. 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. 10. 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. 11. When a feasible region is unbounded and the objective is maximization, the optimal solution: A) Is the origin. B) Does not exist. C) May or may not exist. D) Always exists. Show Answer Correct Answer: C) May or may not exist. 12. What is the optimal solution in LP problems? A) The Solution that Maximizes or Minimizes the Objective Function. B) The Solution that Ignores Constraints. C) The Solution with the Most Variables. D) The Most Complicated Solution. Show Answer Correct Answer: A) The Solution that Maximizes or Minimizes the Objective Function. 13. What is the condition for the variables in a linear programming problem? A) Negative. B) Zero. C) Fractional. D) Non-negative. Show Answer Correct Answer: D) Non-negative. 14. Larry's Fish Market buys salmon (S) for $ 5 per pound and a local whitefish (W) for $ 3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $ 160. The objective function that minimizes these costs for Larry is: A) Min 5S + 3.5 W. B) Min 5S + 3.5W = 160. C) 5S + 3.5W = 160. D) Max 5S + 3.5 W. Show Answer Correct Answer: A) Min 5S + 3.5 W. 15. Question 2:How is the feasible region determined in a linear programming problem? A) By plotting the constraints on a graph and finding the overlapping area. B) By using trial and error to find the region. C) By randomly selecting a region on the graph. D) By solving a system of linear equations. Show Answer Correct Answer: A) By plotting the constraints on a graph and finding the overlapping area. 16. What is the main goal of linear programming? A) To reduce the number of products. B) To eliminate all constraints. C) To minimize costs. D) To increase the number of employees. Show Answer Correct Answer: C) To minimize costs. 17. Which field widely uses linear programming to make efficient use of resources and achieve specific goals? A) Engineering. B) Agriculture. C) Medicine. D) Business. Show Answer Correct Answer: D) Business. 18. What is the role of GeoGebra in teaching graphical solutions to linear inequalities? A) Analyzing historical data. B) Enhancing visual learning experiences. C) Creating music compositions. D) Predicting future trends. Show Answer Correct Answer: B) Enhancing visual learning experiences. 19. How can graphical solutions help in optimizing production planning? A) By Ignoring Constraints. B) By Increasing Costs. C) By Decreasing Efficiency. D) By Maximizing Output. Show Answer Correct Answer: D) By Maximizing Output. 20. What is the objective function in a linear programming problem? A) A function that is only defined for integers. B) A function that needs to be minimized or maximized. C) A function that is always linear. D) A function that has no constraints. Show Answer Correct Answer: B) A function that needs to be minimized or maximized. 21. For converting a problem in to dual, minimization primal should have A) All constraints greater than equal to. B) All constraints less than equal to. C) All constraints equal to. D) None of these. Show Answer Correct Answer: B) All constraints less than equal to. 22. This mathematical symbol ' < ' is represent the following EXCEPT:Simbol matematik "<" mewakili pilihan di bawah KECUALI: A) Fewer than. B) Less than. C) Exceeds. D) Below. Show Answer Correct Answer: C) Exceeds. 23. Determine if the system of equations 3x + 2y = 6 and 6x + 4y = 12 is consistent. A) The system has no solutions. B) No, the system is inconsistent. C) The equations represent parallel lines. D) Yes, the system is consistent. Show Answer Correct Answer: D) Yes, the system is consistent. 24. What are the limitations of linear programming in decision making processes? A) Assumption of linearity, requirement of known parameters, inability to handle discrete decisions, challenge of dealing with multiple objectives. B) Unlimited flexibility in decision-making. C) Ability to incorporate uncertain parameters. D) Ease of handling complex models. Show Answer Correct Answer: A) Assumption of linearity, requirement of known parameters, inability to handle discrete decisions, challenge of dealing with multiple objectives. 25. How do you determine the optimal solution using the graphical method? A) Identify the optimal point in the feasible region by evaluating corner points of the constraints. B) Identify the optimal point by averaging all corner points of the constraints. C) Choose any point within the feasible region without evaluating constraints. D) Select the midpoint of the feasible region as the optimal solution. Show Answer Correct Answer: A) Identify the optimal point in the feasible region by evaluating corner points of the constraints. 26. What is the role of the pivot element in the simplex method? A) Intersection of the pivot row and pivot column. B) Value of the objective function. C) Value of the basic variables. D) Value of the non-basic variables. Show Answer Correct Answer: A) Intersection of the pivot row and pivot column. 27. The distinguishing feature of an LP model is A) Relationship among all variables is linear. B) It has single objective function and constraints. C) Value of decision variables is nonnegative. D) All of the above. Show Answer Correct Answer: D) All of the above. 28. Maps, blueprints and programs are examples of which model A) Digital. B) Symbolic. C) Iconic. D) Analog. Show Answer Correct Answer: D) Analog. 29. How do you handle multiple optimal solutions in graphical methods? A) Ignore the feasible region entirely. B) Identify all points on the objective function line tangent to the feasible region. C) Use only the corner points of the feasible region. D) Select only the highest point on the graph. Show Answer Correct Answer: B) Identify all points on the objective function line tangent to the feasible region. 30. What does it mean for a solution region to be bounded? A) It has no constraints. B) It can be enclosed in a rectangle. C) It contains only one point. D) It is infinite in size. Show Answer Correct Answer: B) It can be enclosed in a rectangle. 31. What are the coordinates of the vertex at the intersection of x + y = 5 and 2x + 3y = 12? A) (0, 5). B) (6, 0). C) (5, 5). D) (3, 2). Show Answer Correct Answer: D) (3, 2). 32. Linear Programming provides a method to optimize operations within certain constraints. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 33. Resources are what you use to create your product. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 34. What is the optimal value of a linear function in a linear programming problem? A) Minimum value. B) Maximum value. C) Median value. D) Average value. Show Answer Correct Answer: A) Minimum value. 35. A company makes two products, A and B. Each A requires 2 hours of labor and 3 units of material. Each B requires 1 hour of labor and 2 units of material. The company has 100 hours of labor and 120 units of material available. Which system represents the constraints? A) $2x + 3y \leq 100$ $1x + 2y \leq 120$. B) $2x + 3y \leq 100$ $1x + 2y \leq 120$. C) $2x + 1y \leq 100$ $3x + 2y \leq 120$. D) $2x + 1y \leq 120$ $3x + 2y \leq 100$. Show Answer Correct Answer: C) $2x + 1y \leq 100$ $3x + 2y \leq 120$. 36. Objective quantity:30x + 50yCorner Points:(0, 0) (8, 0) (6, 2) (0, 6)What is the maximum profit? A) 400. B) 300. C) 240. D) 280. Show Answer Correct Answer: B) 300. 37. Solve.-5|4 +n| <-15 A) N >-1 or n <-7. B) No solution. C) N > 1 or n <-7. D) -7 < n <-1. Show Answer Correct Answer: A) N >-1 or n <-7. 38. How can LP be applied in healthcare according to the text? A) To optimize production planning. B) To optimize investment portfolios. C) To optimize transportation routes. D) To optimize staff scheduling in hospitals. Show Answer Correct Answer: D) To optimize staff scheduling in hospitals. 39. What are the rules that limit our choices called? A) Recommendations. B) Guidelines. C) Preferences. D) Constraints. Show Answer Correct Answer: D) Constraints. 40. Consider the following linear programming problem:Maximize Z = 12x + 10y Subject to:$4x+3y\le480$ $\\2x+3y\le360$ $x\ge0$ $y\ge0$ A) (60, 80). B) (120, 0). C) (180, 120). D) None of the above. Show Answer Correct Answer: A) (60, 80). 41. Acquiring input data is part of: A) Model formulation or solution. B) Model identification. C) Model testing. D) Model interpretation. Show Answer Correct Answer: A) Model formulation or solution. 42. In the example provided, what is the profit from producing one unit of product A? A) $ 40. B) $ 60. C) $ 50. D) $ 30. Show Answer Correct Answer: C) $ 50. 43. Interpret the optimal solution for the problem:Minimize z = 2x + 5y with the constraints:3x + 4y $\geq$ 12, x $\geq$ 0, y $\geq$ 0. A) The optimal solution is at (0, 3) with a minimum value of z = 15. B) The optimal solution is at (1, 2) with a minimum value of z = 29. C) The optimal solution is at (4, 0) with a minimum value of z = 8. D) The optimal solution is at (2, 2) with a minimum value of z = 18. Show Answer Correct Answer: C) The optimal solution is at (4, 0) with a minimum value of z = 8. 44. What does the feasible region represent in linear programming? A) Set of all possible solutions that satisfy the constraints. B) Region where the objective function is maximized. C) Area where all constraints are violated. D) Set of points with no feasible solutions. Show Answer Correct Answer: A) Set of all possible solutions that satisfy the constraints. 45. What are the variables in a linear programming problem sometimes called? A) Independent variables. B) Random variables. C) Decision variables. D) Dependent variables. Show Answer Correct Answer: C) Decision variables. 46. Linear programming A) An apparent solution that must be rejected because it does not satisfy the original equation. B) The process of finding the maximum or minimum values of a function for a region defined by inequalities. C) The intersection of the graphs in a system of constraints. D) Written |x|, the distance the number is from 0 on a number line. Show Answer Correct Answer: B) The process of finding the maximum or minimum values of a function for a region defined by inequalities. 47. If the objective function is maximized at a vertex of the feasible region, what does this imply? A) The optimal solution is always at an edge of the feasible region. B) The optimal solution is at the center of the feasible region. C) The optimal solution cannot be at a vertex. D) The optimal solution is at a vertex of the feasible region. Show Answer Correct Answer: D) The optimal solution is at a vertex of the feasible region. 48. Graph the inequality 2x-y $\geq$ 4 and shade the feasible region. A) Graph the line y = 2x-4 with a dashed line and shade the region above it. B) Graph the line y = 2x-4 with a solid line and shade the region below it. C) Graph the line y =-2x + 4 with a solid line and shade the region below it. D) Graph the line y = 2x + 4 with a dashed line and shade the region above it. Show Answer Correct Answer: B) Graph the line y = 2x-4 with a solid line and shade the region below it. 49. Determine if the system of equations x + 2y = 4 and 2x + 4y = 8 is consistent. A) Yes, the system is consistent. B) The system has no solutions. C) No, the system is inconsistent. D) The equations represent parallel lines. Show Answer Correct Answer: A) Yes, the system is consistent. 50. How can retail companies benefit from linear programming techniques? A) Optimizing financial reporting. B) Optimizing customer service. C) Optimizing supply chain operations. D) Optimizing production planning. Show Answer Correct Answer: D) Optimizing production planning. 51. The LPP is solved graphically when it has: A) Two decision variables. B) One equation only. C) Four objective functions. D) Two constraints. Show Answer Correct Answer: A) Two decision variables. 52. Yang mana merupakan fungsi linear? $xy$ A) $xy$. B) $y=2x^2$. C) $y=2x$. D) $x$. Show Answer Correct Answer: C) $y=2x$. 53. What is the graphical method used for in linear programming? A) To determine the constraints of the problem. B) To calculate the objective function. C) To visually represent the feasible region and find the optimal solution. D) To identify the decision variables. Show Answer Correct Answer: C) To visually represent the feasible region and find the optimal solution. 54. Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 55. What should be done after finding the optimal solution in LP using Excel? A) Ignore the Results. B) Start Over. C) Delete the Spreadsheet. D) Conduct Sensitivity Analysis. Show Answer Correct Answer: D) Conduct Sensitivity Analysis. 56. Which of the following is NOT a characteristic of LP A) Finiteness. B) Growth. C) Non-Negativity. D) Decision Variable. Show Answer Correct Answer: B) Growth. 57. Graph and identify a possible solution.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). 58. A constraint in linear programming must be expressed as: A) A non-linear equation. B) An objective function. C) A linear equation or inequality. D) A random variable. Show Answer Correct Answer: C) A linear equation or inequality. 59. If any variable of the primal problem is unrestricted in sign, then the corresponding constraint in the dual problem will be ..... type. A) $=$. B) $\le$. C) $<$. D) $\ge$. Show Answer Correct Answer: A) $=$. 60. Solve the optimization problem:Maximize 3x + 4y subject to the constraints x >= 0, y >= 0, and 2x + y <= 10. A) 14. B) 12. C) 16. D) 15. Show Answer Correct Answer: D) 15. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 12 Linear Programming Quiz 1Class 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 8Class 12 Mathematics Chapter 12 Linear Programming Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books