This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 4 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. How can graphical methods be used in linear programming? A) Graphical methods are used to calculate numerical values in linear programming. B) Graphical methods help visualize constraints and find optimal solutions in linear programming. C) Graphical methods eliminate the need for constraints in linear programming. D) Graphical methods are primarily used for non-linear programming problems. Show Answer Correct Answer: B) Graphical methods help visualize constraints and find optimal solutions in linear programming. 2. Which of the following is a common application of NLP in Inventory Management? A) Optimizing inventory levels where holding costs are non-linear. B) Selecting the fastest production machinery. C) Determining the ideal number of employees for a shift. D) Finding the shortest distance between two warehouses. Show Answer Correct Answer: A) Optimizing inventory levels where holding costs are non-linear. 3. It help us to visualize the procedure of finding the optimal solution to a linear programming problem. A) Feasible Region. B) Linear Programming. C) Corner point Method. D) Graphical Method. Show Answer Correct Answer: D) Graphical Method. 4. Which of these is a constraint type in LPP? A) Quadratic inequality. B) Linear equality or inequality. C) Exponential function. D) None of the above. Show Answer Correct Answer: B) Linear equality or inequality. 5. Identify the feasible region for the inequalities x >= 0, y >= 0, and 3x + 2y <= 12. A) The feasible region is a square with vertices at (0, 0), (0, 12), (12, 0), and (12, 12). B) The feasible region is a circle with center at (0, 0) and radius 6. C) The feasible region is a triangle with vertices at (0, 0), (0, 6), and (4, 0). D) The feasible region is a line segment with endpoints at (0, 0) and (6, 0). Show Answer Correct Answer: C) The feasible region is a triangle with vertices at (0, 0), (0, 6), and (4, 0). 6. What is the objective function in a linear programming model? A) The numeric values in the constraints. B) A linear mathematical relationship that describes the objective of the firm. C) A set of restrictions placed on the firm by the operating environment. D) The last point the objective function touches as it leaves the feasible solution area. Show Answer Correct Answer: B) A linear mathematical relationship that describes the objective of the firm. 7. The solution of a system of three linear equations in three variables, x, y, and z, is called a(n) ..... (x, y, z). A) Ordered Pair. B) Ordered Triple. C) Sum. D) Integer. Show Answer Correct Answer: B) Ordered Triple. 8. What is the final step in formulating a linear programming model? A) Solving the LP model. B) Identifying the objective. C) Identifying decision variables. D) Writing the LP model. Show Answer Correct Answer: D) Writing the LP model. 9. Nonnegativity constraints ensure that A) The objective function of the problem always returns maximum quantities. B) There are no inequalities in the constraints. C) The problem modeling includes only nonnegative values in the constraints. D) The solution to the problem will contain only nonnegative values for the decision variables. Show Answer Correct Answer: D) The solution to the problem will contain only nonnegative values for the decision variables. 10. Solve. Show all work. 10(h+1)-4=76 A) H=10. B) H=76. C) H=4. D) H=7. Show Answer Correct Answer: D) H=7. 11. Sarah makes $ 30 for each small purse (x) and $ 50 for each big purse (y). What is the objective function? A) Z = 30x + 50y. B) Z = 50x + 30y. C) All the above. D) None of the above. Show Answer Correct Answer: A) Z = 30x + 50y. 12. How can LP be used in optimizing supply chain operations? A) Managing investment portfolios. B) Determining optimal production levels. C) Optimizing transportation routes. D) Allocating resources in hospitals. Show Answer Correct Answer: B) Determining optimal production levels. 13. In the Flair Furniture example, what is the maximum number of chairs that can be produced? A) 60. B) 40. C) 80. D) 100. Show Answer Correct Answer: A) 60. 14. A method for solving a problem with several conditions or constraints that can be represented as linear equations or inequalities. A) Linear programming. B) Looking inside. C) Maximize. D) One-variable equation. Show Answer Correct Answer: A) Linear programming. 15. Interpret the objective function in the context of a profit maximization problem where x represents the quantity of product sold and y represents the price per unit. A) The objective function is:Revenue = x * y. B) Objective function:Sales = x-y. C) Objective function:Profit = x / y. D) Objective function:Cost = x + y. Show Answer Correct Answer: A) The objective function is:Revenue = x * y. 16. What is a feasible solution in the context of linear programming? A) A random guess for decision variables. B) A set of values that violates at least one constraint. C) A set of values for decision variables that satisfies all constraints. D) Any arbitrary selection of decision variables. Show Answer Correct Answer: C) A set of values for decision variables that satisfies all constraints. 17. A baker is using the function $P=2.5x+2y$ $x\ge0$ $y\ge0$ $3x+y\le9$ $2x+4y\le16$ A) 2 cakes and 3 cookies. B) 3 cakes and 2 cookies. C) 0 cakes and 4 cookies. D) 4 cakes and 0 cookies. Show Answer Correct Answer: A) 2 cakes and 3 cookies. 18. When using Solver, the parameter Changing Cells is typically associated with the objective function. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: B) FALSE. 19. What is the primary objective of linear programming in forest-based industries? A) Minimize timber yield. B) Maximize environmental impact. C) Optimize resource allocation. D) Increase inventory holding costs. Show Answer Correct Answer: C) Optimize resource allocation. 20. How does the graphical method of solving linear programming problems help in decision-making? A) By memorizing complex equations. B) By ignoring constraints. C) By guessing the optimal solution. D) By visually representing constraints and the objective function. Show Answer Correct Answer: D) By visually representing constraints and the objective function. 21. The point where two constraints intersect is called a: A) Slope. B) Gradient. C) Corner point. D) Maximum value. Show Answer Correct Answer: C) Corner point. 22. What is the primary advantage of LP in optimizing production processes? A) Maximizing confusion. B) Maximizing losses. C) Maximizing efficiency. D) Maximizing costs. Show Answer Correct Answer: C) Maximizing efficiency. 23. Provide an example of a real-world application of linear programming. A) Supply chain management. B) Hospital scheduling. C) Weather forecasting. D) Agricultural planning. Show Answer Correct Answer: A) Supply chain management. 24. What does LPP stand for? A) Linear Programming Problem. B) Local Projection Problem. C) Logistic Planning Procedure. D) Linear Probability Process. Show Answer Correct Answer: A) Linear Programming Problem. 25. Solve the optimization problem:Minimize 2x + 5y subject to the constraints x >= 0, y >= 0, and x + 2y <= 8. A) The minimum value of the objective function 2x + 5y is 15. B) The minimum value of the objective function 2x + 5y is 20. C) The constraints x >= 0, y >= 0, and x + 2y <= 8 are infeasible. D) The solution to the optimization problem is x = 3, y = 2. Show Answer Correct Answer: B) The minimum value of the objective function 2x + 5y is 20. 26. What is LP used for in inventory management in forest-based industries? A) Increase stockouts of finished goods. B) Optimize inventory levels while minimizing costs. C) Maximize inventory holding costs. D) Minimize raw material availability. Show Answer Correct Answer: B) Optimize inventory levels while minimizing costs. 27. What is the Simplex Method used for in linear programming? A) Creating graphs. B) Finding the profit from products. C) Solving linear programming problems with more than two variables. D) Allocating resources. Show Answer Correct Answer: C) Solving linear programming problems with more than two variables. 28. Identify if the function j(x) = sin(x) is onto when the codomain is [-1, 1]. Explain your answer. A) No, the function j(x) = sin(x) is onto only for the codomain [0, 1]. B) Yes, the function j(x) = sin(x) is onto when the codomain is (-1, 1). C) Yes, the function j(x) = sin(x) is onto when the codomain is [-1, 1]. D) No, the function j(x) = sin(x) is not onto when the codomain is [-1, 1]. Show Answer Correct Answer: C) Yes, the function j(x) = sin(x) is onto when the codomain is [-1, 1]. 29. What are the key components of a linear programming model? A) Variables, objective function, boundaries, non-positivity constraints. B) Variables, goal function, limitations, positivity constraints. C) Variables, target function, restrictions, non-negativity constraints. D) Decision variables, objective function, constraints, non-negativity constraints. Show Answer Correct Answer: D) Decision variables, objective function, constraints, non-negativity constraints. 30. Indicate whether the statement is true or false.1. Only binding constraints form the shape (boundaries) of the feasible region. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 31. How can LP be used in finance according to the text? A) To optimize production planning. B) To optimize transportation routes. C) To optimize supply chain operations. D) To optimize investment portfolios. Show Answer Correct Answer: D) To optimize investment portfolios. 32. Which software tool, known for large-scale optimization, is listed as a tool for solving NLP problems? A) Microsoft Word. B) GAMS (General Algebraic Modeling System). C) Microsoft Excel (without add-ins). D) Adobe Photoshop. Show Answer Correct Answer: B) GAMS (General Algebraic Modeling System). 33. The common region represented by $x-y\le3$ $2x+y\le5$ $x\le2$ $x\ge0$ A) First quadrant. B) First and second quadrants. C) Third quadrant. D) Second and third quadrants. Show Answer Correct Answer: D) Second and third quadrants. 34. Solve $-2\left(x+1\right)\le3\left(x+1\right)$ A) $x\ge5$. B) $x\ge-5$. C) $x\le1$. D) $x\ge-$. Show Answer Correct Answer: D) $x\ge-$. 35. In LPP, the region bounded by all the constraints is called: A) Polygon. B) Objective zone. C) Constant area. D) Feasible region. Show Answer Correct Answer: D) Feasible region. 36. The term "optimal solution" refers to: A) Any solution in the feasible region. B) The maximum or minimum value of the objective function. C) The origin. D) None of these. Show Answer Correct Answer: B) The maximum or minimum value of the objective function. 37. In LPP, if no point satisfies all constraints, the problem is said to be: A) Degenerate. B) Unbounded. C) Infeasible. D) Feasible. Show Answer Correct Answer: C) Infeasible. 38. Graph the inequality x-y > 2 and shade the appropriate region. A) Graph the line y = x-2 as a solid line and shade the region above it. B) Graph the line y =-x + 2 as a dashed line and shade the region to the left of it. C) Graph the line y = x-2 as a dashed line and shade the region below it. D) Graph the line y = x + 2 as a solid line and shade the region above it. Show Answer Correct Answer: C) Graph the line y = x-2 as a dashed line and shade the region below it. 39. How can LP be used in environmental studies according to the text? A) To optimize production planning. B) To optimize investment portfolios. C) To optimize waste management strategies. D) To optimize transportation routes. Show Answer Correct Answer: C) To optimize waste management strategies. 40. The graphical method of solving LPP can be applied only when: A) There are two decision variables. B) Variables are integers. C) Objective function is nonlinear. D) There are three constraints. Show Answer Correct Answer: A) There are two decision variables. 41. How can an initial feasible solution be obtained in transportation problem? A) Northwest Corner Method. B) Least Cost Method. C) Vogel's Approximation Model. D) All of the above. Show Answer Correct Answer: D) All of the above. 42. Kursus X dan kursus Y diadakan dalam suatu program.I) Kapasiti program adalah 170 orangII) Jumlah minimum pengambilan program adalah 80 orangIII) Bilangan kursus Y adalah melebihi dua kalibilangan kursus X sekurang-kurangnya 20 orangTentukan ketaksamaan yang betul: A) $x+y\le170$ $x+y\ge80$ $x-y\ge20$. B) $x+y\le170$ $x+y\ge80$ $y-x\ge20$. C) $x+y\ge170$ $x+y\le80$ $y+x\ge20$. D) $x+y\le170$ $x+y\le80$ $y\ge x+20$. Show Answer Correct Answer: B) $x+y\le170$ $x+y\ge80$ $y-x\ge20$. 43. Define feasible region. A) A collection of all possible solutions. On the graph, it is where the shading overlaps. B) Limits put on possible outcomes. C) Money you make, after expenses. D) Vertices where the lines intersect. Show Answer Correct Answer: A) A collection of all possible solutions. On the graph, it is where the shading overlaps. 44. Why do manufacturing companies use graphical solutions in production planning? A) To manage inventory levels efficiently. B) To optimize production capacities. C) To visually analyze feasible production levels. D) All of the above. Show Answer Correct Answer: D) All of the above. 45. If you buy pens ($ 0.55 each) and a binder ($ 2.39) and only have $ 10 in your pocket, which inequality can help you figure out how many pens you can buy? A) 10 < 0.55x-2.39. B) 10 < 0.55x + 2.39. C) 10 $\geq$ 0.55x + 2.39. D) 10 $\geq$ 0.55x-2.39. Show Answer Correct Answer: C) 10 $\geq$ 0.55x + 2.39. 46. Jika anda menyalip 2 orang diposisi terakhir, kemudian 1 orang di belakang anda menyalip. Anda sekarang diposisi berapa?? A) Terakhir. B) Kedua dari terakhir. C) Ketiga dari terakhir. D) Tidak perlu dijawab hehehe . E) Semua salah. Show Answer Correct Answer: E) Semua salah. 47. Optimization Equation:P = 30x + 50yCorner that maximizes profit:(0, 6)What is the profit? A) 280. B) 300. C) 400. D) 240. Show Answer Correct Answer: B) 300. 48. Which vertex is NOT one of the vertices of the feasible region? A) (6, 0). B) (0, 0). C) (0, 8). D) (3, 6). E) (4, 8). Show Answer Correct Answer: E) (4, 8). 49. How do you find the y-intercept of the line 2x + 3y = 12? A) Set x to 0 and solve for y. B) Set both x and y to 0. C) Set y to 0 and solve for x. D) Set x to 1 and solve for y. Show Answer Correct Answer: A) Set x to 0 and solve for y. 50. Graph the linear equation 3x + 2y = 6. A) Y =-3x + 4. B) Y =-1.5x + 3. C) Y = 0.5x + 2. D) Y = 2x + 1. Show Answer Correct Answer: B) Y =-1.5x + 3. 51. Which method is used to graphically solve an LP problem? A) Trial and error method. B) Random selection method. C) Iso-profit line method. D) Cost-benefit analysis. Show Answer Correct Answer: C) Iso-profit line method. 52. Ani membeli 2 buku dan 1 pensil seharga Rp14.000. Budi membeli 1 buku dan 2 pensil seharga Rp11.000. Jika harga buku = x dan harga pensil = y, maka nilai x adalah ..... A) 6000. B) 4000. C) 7000. D) 5000. Show Answer Correct Answer: A) 6000. 53. Other name of MODI method A) U-u method. B) U-v method. C) V-v method. D) None. Show Answer Correct Answer: B) U-v method. 54. These are restrictions placed on the firm by the operations of the organizations such as working hours and resources. A) DECISION VARIABLE. B) CONSTRAINTS. C) PARAMETERS. D) OBJECTIVE FUNCTION. Show Answer Correct Answer: B) CONSTRAINTS. 55. What is the objective of Session 10.1? A) Teaching Algebraic Equations. B) Teaching Trigonometry. C) Teaching Probability. D) Teaching Graphical Solutions to Linear Inequalities. Show Answer Correct Answer: D) Teaching Graphical Solutions to Linear Inequalities. 56. The importance of ..... for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution. A) Optimization analysis. B) Objective function. C) Sensitivity analysis. D) Decision variables. Show Answer Correct Answer: C) Sensitivity analysis. 57. How is the optimal solution determined in linear programming using the graphical method? A) By finding the point of intersection of the feasible region that maximizes or minimizes the objective function. B) By selecting the point of intersection that is closest to the origin. C) By choosing the point of intersection that is farthest from the objective function. D) By randomly selecting a point within the feasible region. Show Answer Correct Answer: A) By finding the point of intersection of the feasible region that maximizes or minimizes the objective function. 58. Which of the following is NOT a component of a Linear Programming Problem? A) Profit Margin. B) Decision Variables. C) Objective Function. D) Constraints. Show Answer Correct Answer: A) Profit Margin. 59. What is the purpose of the simplex algorithm in linear programming? A) To draw the graph of constraints. B) To reach the optimal solution through matrix operations. C) To introduce slack variables. D) To identify the leaving variable. Show Answer Correct Answer: B) To reach the optimal solution through matrix operations. 60. Sarah makes $ 30 for each small purse (x) and $ 50 for each big purse (y). What is the optimized solution? A) P = 30x + 50y. B) P = 50x + 30y. C) All the above. D) None of the above. Show Answer Correct Answer: A) P = 30x + 50y. ← 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 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