This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > 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 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the graphical representation of the inequality 3x-2y > 6? A) The graphical representation is a shaded region above the line 3x-2y = 6, excluding the line. B) The graphical representation is a shaded region below the line 3x-2y = 6, including the line. C) The graphical representation is a single point at (2, 0). D) The graphical representation is a dashed line representing the equation 3x-2y = 6. Show Answer Correct Answer: A) The graphical representation is a shaded region above the line 3x-2y = 6, excluding the line. 2. Solve for x |-2n| + 10 =-50 A) No Solution. B) {-5, 5}. C) {30, -30}. D) {20, -20}. Show Answer Correct Answer: A) No Solution. 3. The feasible region for a system of inequalities is the set of all points that: A) Satisfy only one inequality. B) Satisfy all inequalities. C) Do not satisfy any inequality. D) Are outside the boundary lines. Show Answer Correct Answer: B) Satisfy all inequalities. 4. Graph the linear equation 4x-2y = 8. A) Y = 3x-2. B) Y =-2x + 8. C) Y = 4x + 2. D) Y = 2x-4. Show Answer Correct Answer: D) Y = 2x-4. 5. The quantities that are to be determined using decision variable are called A) Decision Variables. B) Constraints. C) Monkey. D) Objective Function. Show Answer Correct Answer: A) Decision Variables. 6. How do you graph the inequality y > 2x-1? A) Graph the line y = 2x-1 as a dashed line and shade above it. B) Graph the line y = 2x-1 and do not shade any area. C) Graph the line y = 2x-1 as a solid line and shade below it. D) Graph the line y = 2x-1 as a dashed line and shade below it. Show Answer Correct Answer: A) Graph the line y = 2x-1 as a dashed line and shade above it. 7. Dani 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, Dani made a total of $ 78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation? A) 1.5x+0.5y=78.51.5x+0.5y=87. B) 1.5x+0.5y=78.5x+y=87. C) X+y=78.51.5x+0.5y=87. D) X+y=78.5x+y=87. Show Answer Correct Answer: B) 1.5x+0.5y=78.5x+y=87. 8. In dealing with business models, managers need to consider only quantitative data while making decisions in practice. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: B) FALSE. 9. Sebuah perusahaan ojek online menetapkan biaya awal Rp5.000 dan Rp2.000 setiap kilometer. Jika dinyatakan sebagai fungsi linear y=mx+c, maka m dan c berturut-turut adalah ..... A) 2 dan 5. B) 5 dan 2. C) 5000 dan 2000. D) 2000 dan 5000. Show Answer Correct Answer: D) 2000 dan 5000. 10. A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $ 370, and the cost of joining for 6 months is $ 530. Write a system of equations to find the registration fee and monthly fee. m= months; r = registration fee. A) M-4r = 370m-6r = 530. B) R-4m = 370r-6m = 530. C) M + 4r = 370m + 6r = 530. D) R + 4m = 370r + 6m = 530. Show Answer Correct Answer: D) R + 4m = 370r + 6m = 530. 11. Interpret the optimal solution for the problem:Minimize z = x + 2y with the constraints:3x + 4y $\geq$ 12, x $\geq$ 0, y $\geq$ 0. A) The optimal solution is at (2, 3) with a minimum value of z = 8. B) The optimal solution is at (4, 0) with a minimum value of z = 4. C) The optimal solution is at (1, 5) with a minimum value of z = 11. D) The optimal solution is at (0, 6) with a minimum value of z = 12. Show Answer Correct Answer: B) The optimal solution is at (4, 0) with a minimum value of z = 4. 12. How can the graphical method of solving LP problems be useful in different sectors? A) It is limited to academic exercises. B) It only works in theoretical scenarios. C) It can optimize supply chain operations, production levels, and transportation routes. D) It has no practical applications outside of mathematics. Show Answer Correct Answer: C) It can optimize supply chain operations, production levels, and transportation routes. 13. LP theory states that the optimal solution to any problem will lie 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. 14. What is an optimum value? A) A value that is always negative. B) A value which is either a maximum or a minimum. C) A value that cannot be determined. D) A value that is always positive. Show Answer Correct Answer: B) A value which is either a maximum or a minimum. 15. Rania makes $ 30 for each small purse (x) and $ 50 for each big purse (y). What is the objective quantity? A) 30x + 50y. B) 50x + 30y. C) All the above. D) None of the above. Show Answer Correct Answer: A) 30x + 50y. 16. If the vertices of the feasible region are (0, 0) (2, 5) (6, 2) and (4, 4) which coordinate maximizes an objective function of P=2x+3y A) (6, 2). B) (0, 0). C) (2, 5). D) (4, 4). Show Answer Correct Answer: D) (4, 4). 17. How do you interpret the solution of a linear programming problem graphically? A) The optimal solution is located at a vertex of the feasible region on the graph. B) The solution can be found anywhere within the feasible region. C) The optimal solution is determined by the highest point on the graph. D) The optimal solution is always at the center of the feasible region. Show Answer Correct Answer: A) The optimal solution is located at a vertex of the feasible region on the graph. 18. What is the purpose of the Solver tool in Microsoft Excel for LP problems? A) To create more problems. B) To set up and solve LP problems. C) To confuse students. D) To avoid calculations. Show Answer Correct Answer: B) To set up and solve LP problems. 19. What tool can be used in Microsoft Excel to solve linear programming problems? A) Filter. B) Sort. C) Solver. D) Formula. Show Answer Correct Answer: C) Solver. 20. What do we want to achieve in a linear programming problem? A) To find the maximum number of variables. B) To create a graphical representation of data. C) To optimize a linear objective function subject to constraints. D) To solve non-linear equations. Show Answer Correct Answer: C) To optimize a linear objective function subject to constraints. 21. Which method is commonly used to solve a two-variable linear programming problem graphically? A) Dual Simplex Method. B) Big-M Method. C) Simplex Method. D) Graphical Method. Show Answer Correct Answer: D) Graphical Method. 22. Which of the following is a key assumption of linear programming? A) Non-linearity. B) Discrete variables. C) Proportionality. D) Randomness. Show Answer Correct Answer: C) Proportionality. 23. What are vertices in the context of the feasible region? A) Points where the constraints do not intersect. B) The corner points of the feasible region, where the constraints intersect, and potential solutions to the linear programming problem are evaluated. C) Random points within the feasible region. D) The edges of the feasible region that connect the corner points. Show Answer Correct Answer: B) The corner points of the feasible region, where the constraints intersect, and potential solutions to the linear programming problem are evaluated. 24. What does the graph of a linear inequality divide the plane into? A) A triangle. B) Parabolas. C) Two half-planes. D) Circles. Show Answer Correct Answer: C) Two half-planes. 25. Graph the inequality 3x + 2y < 6 on a coordinate plane. A) Graph the line y = 0.5x-1 as a solid line and shade below it. B) Graph the line y =-1.5x + 3 as a dashed line and shade below it. C) Graph the line y =-2x + 6 as a dashed line and shade above it. D) Graph the line y = 1.5x + 3 as a solid line and shade above it. Show Answer Correct Answer: B) Graph the line y =-1.5x + 3 as a dashed line and shade below it. 26. The solution region in LPP is called A) The vast green field?. B) Unbounded region. C) Feasible region. D) Infeasible region. Show Answer Correct Answer: C) Feasible region. 27. What is an infeasible solution in linear programming? A) An infeasible solution is one that has no variables defined. B) An infeasible solution is one that does not satisfy all constraints in a linear programming problem. C) An infeasible solution is one that maximizes the objective function. D) An infeasible solution is one that satisfies all constraints but is not optimal. Show Answer Correct Answer: B) An infeasible solution is one that does not satisfy all constraints in a linear programming problem. 28. Given the Objective Function is P = 60x + 125y. Find the corner point if thevalue of profit is 1105. A) (7, 5). B) (5, 3). C) (8, 5). D) (8, 9). Show Answer Correct Answer: C) (8, 5). 29. Objective function:P = 30x + 50yThe vertex that maximizes profit is (0, 6). What is the profit? A) $ 300. B) $ 400. C) $ 280. D) $ 240. Show Answer Correct Answer: A) $ 300. 30. Lexie is making apple cobblers and apple pies for a bake sale ..... x= # of cobblers and y is # of piesShe makes $ 6 profit for each cobbler and $ 5 profit for each pie. Select an objective function that models the total profit from cobblers and pies. A) $P=6x+5y$. B) $P=3x+2y$. C) $P=2x+3y$. D) $P=5x+6y$. Show Answer Correct Answer: A) $P=6x+5y$. 31. Which application involves determining the best way to allocate resources? A) Resource Allocation. B) Solution Methods. C) Diet Problems. D) Production Scheduling. Show Answer Correct Answer: A) Resource Allocation. 32. What is a key advantage of using NLP over Linear Programming (LP) in supply chain modeling? A) NLP is less computationally intensive. B) LP cannot handle continuous variables. C) NLP provides better modeling of reality by capturing non-linear relationships. D) The results of NLP are easier to interpret. Show Answer Correct Answer: C) NLP provides better modeling of reality by capturing non-linear relationships. 33. An objective function in a linear program can be which of the following? A) An uncertain quantity. B) A maximization function. C) A quadratic maximization function. D) A nonlinear maximization function. Show Answer Correct Answer: B) A maximization function. 34. In the graphical method, what does the feasible region represent? A) Infeasible solutions. B) Randomly generated points. C) Only the optimal solution. D) All possible solutions that satisfy the constraints. Show Answer Correct Answer: D) All possible solutions that satisfy the constraints. 35. What is meant by 'divisibility' in linear programming? A) Decision variables can take any fractional value. B) Variables must be whole numbers. C) Decision variables can only be whole numbers. D) Only integers can be used. Show Answer Correct Answer: A) Decision variables can take any fractional value. 36. If a linear programming problem has more than one optimal solution, it is called: A) Degenerate. B) Infeasible. C) Unbounded. D) Multiple optimal solutions. Show Answer Correct Answer: D) Multiple optimal solutions. 37. How can you verify the solution obtained from the graphical method in linear programming? A) Substitute values back into the objective function and constraints to verify the solution. B) Use a different graphical method to verify. C) Check if the solution is the same as the initial guess. D) Ask a friend to confirm the solution. Show Answer Correct Answer: A) Substitute values back into the objective function and constraints to verify the solution. 38. In Phase 1, if Max Z* $<$ A) Basic solution. B) Optimum solution. C) Feasible solution. D) No feasible solution. Show Answer Correct Answer: D) No feasible solution. 39. How can LP be applied in finance? A) To Predict Weather Patterns. B) To Write Poetry. C) To Design Buildings. D) To Optimize Investment Portfolios. Show Answer Correct Answer: D) To Optimize Investment Portfolios. 40. Which method is used for solving linear models? A) Graphical. B) Simplex. C) Solver. D) All. Show Answer Correct Answer: D) All. 41. How do you identify feasible solutions in a graphical method? A) Feasible solutions are found by calculating the objective function value. B) Feasible solutions are determined by selecting random points on the graph. C) Feasible solutions are identified by drawing only the objective function line. D) Feasible solutions are identified by plotting constraints and finding the overlapping feasible region. Show Answer Correct Answer: D) Feasible solutions are identified by plotting constraints and finding the overlapping feasible region. 42. What is the purpose of conducting sensitivity analysis in linear programming? A) To confuse students. B) To skip steps in the process. C) To understand how changes impact the optimal solution. D) To avoid solving problems. Show Answer Correct Answer: C) To understand how changes impact the optimal solution. 43. How can LP be used in supply chain operations? A) None of the above. B) To optimize production levels. C) To allocate resources effectively. D) To determine transportation routes. Show Answer Correct Answer: C) To allocate resources effectively. 44. Explain the significance of the feasible region in a linear programming problem. A) The feasible region is the area where no solutions exist. B) The feasible region only includes the optimal solution. C) The feasible region is irrelevant to the optimization process. D) The feasible region represents all possible solutions that satisfy the constraints. Show Answer Correct Answer: D) The feasible region represents all possible solutions that satisfy the constraints. 45. Find the inverse of the matrix [[5, 7], [2, 3]]. A) [[3, -7], [-2, 5]]. B) [[1, 2], [3, 4]]. C) [[0, 1], [1, 0]]. D) [[5, 3], [2, 7]]. Show Answer Correct Answer: A) [[3, -7], [-2, 5]]. 46. What is one benefit of linear programming for forest-based industries? A) Increased waste and inefficiencies. B) Reduced decision-making based on intuition. C) Enhanced sustainability through optimized resource allocation. D) Ignoring environmental constraints. Show Answer Correct Answer: C) Enhanced sustainability through optimized resource allocation. 47. Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the corner points? $x+y\le8$ $5x-7y\ge-14$ $y\ge2$ A) (2, 0), (4, 5), (6, 0). B) (0, 2), (3.5, 4.5), (6, 2). C) (0, 0), (3, 5), (6, 0). D) (2, 0), (3, 5), (0, 6). Show Answer Correct Answer: B) (0, 2), (3.5, 4.5), (6, 2). 48. Which of the following is NOT a component of a linear programming model? A) Random variables. B) Decision variables. C) Objective function. D) Constraints. Show Answer Correct Answer: A) Random variables. 49. Constraints are what you are using to create your product. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 50. What is the main application of LP in supply chain operations? A) Optimizing Staff Scheduling. B) Minimizing Profit. C) Maximizing Fuel Consumption. D) Determining Transportation Routes. Show Answer Correct Answer: D) Determining Transportation Routes. 51. In any balanced transportation problem with m sources n destinations, there have to be ..... basic cells A) $m-n+1$. B) $m+n-2$. C) $m+n+1$. D) $m+n-1$. Show Answer Correct Answer: D) $m+n-1$. 52. Which of the following is NOT a step in LPP formulation? A) Writing constraints. B) Ignoring objective function. C) Writing objective function. D) Defining variables. Show Answer Correct Answer: B) Ignoring objective function. 53. How many of each purse should Sarah make to maximize profit? A) 6 big purses. B) 8 small purses. C) 6 small purses and 2 big purses. D) None of the above. Show Answer Correct Answer: A) 6 big purses. 54. In graphical method, the feasible region is plotted on: A) Bar graph. B) Number line. C) Pie chart. D) XY-plane. Show Answer Correct Answer: D) XY-plane. 55. Which of the following statements best describes the simplex method when applied to optimizing a portfolio in finance? A) A method that visually identifies the optimal portfolio mix. B) A trial-and-error method for finding the feasible investment region. C) An algorithm that systematically moves through portfolio options to find the optimal investment solution. D) A method that only works for portfolios with two types of assets. Show Answer Correct Answer: C) An algorithm that systematically moves through portfolio options to find the optimal investment solution. 56. Which mathematical tool uses the second-order derivative (the Hessian matrix) to potentially find the minimum or maximum faster than gradient descent? A) Simplex Method. B) Newton's Method. C) Lagrange Multipliers. D) Monte Carlo Simulation. Show Answer Correct Answer: B) Newton's Method. 57. What is the role of parameters in a linear programming model? A) To set constraints. B) To provide numerical coefficients and constants. C) To define the objective function. D) To represent decision variables. Show Answer Correct Answer: B) To provide numerical coefficients and constants. 58. Solve the optimization problem:Minimize 2x + 4y subject to the constraints x >= 0, y >= 0, and 3x + y <= 12. A) The solution is x = 3, y = 2. B) The constraints are not feasible. C) The minimum value is 10. D) The minimum value of 2x + 4y subject to the constraints x >= 0, y >= 0, and 3x + y <= 12 is 8. Show Answer Correct Answer: D) The minimum value of 2x + 4y subject to the constraints x >= 0, y >= 0, and 3x + y <= 12 is 8. 59. The optimum solution of an LPP, if exists, lies: A) Outside the feasible region. B) At the origin. C) At a vertex of the feasible region. D) At any interior point. Show Answer Correct Answer: C) At a vertex of the feasible region. 60. What is the main benefit of using Microsoft Excel to solve LP problems? A) It Increases Complexity. B) It Provides Visual Representations. C) It Causes Errors. D) It Solves Problems Instantly. Show Answer Correct Answer: B) It Provides Visual Representations. ← 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 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