This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 12 Linear Programming – Quiz 11 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 12 Linear Programming Quiz 11 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. 2x-y = 04x-y = 0 A) Infinite Solutions. B) No Solutions. C) (1, 2). D) (0, 0). Show Answer Correct Answer: D) (0, 0). 2. Does linear programming require computer programming to solve problems? A) Yes. B) No. C) All the above. D) None of the above. Show Answer Correct Answer: B) No. 3. Question 9:Can the feasible region change if the constraints of a linear programming problem are altered? Explain. A) Yes. B) Maybe. C) No. D) Only if the objective function changes. Show Answer Correct Answer: A) Yes. 4. What are the two types of distribution models? A) Transportation and assignment. B) Linear and non-linear. C) Feasible and infeasible. D) Optimal and suboptimal. Show Answer Correct Answer: A) Transportation and assignment. 5. How can you determine the optimal solution using a graph? A) Use linear programming to find the optimal solution. B) Apply random sampling to estimate the best path. C) Rely on trial and error to determine the best route. D) Use graph algorithms like Dijkstra's or Prim's to find the optimal solution. Show Answer Correct Answer: D) Use graph algorithms like Dijkstra's or Prim's to find the optimal solution. 6. What is the first step in graphing a linear inequality? A) Rewrite the inequality in slope-intercept form. B) Solve for x. C) Find the area of the inequality region. D) Plot the y-intercept on the graph. Show Answer Correct Answer: A) Rewrite the inequality in slope-intercept form. 7. The common region represented by the inequalities $3x+5y\le15$ $5x+2y\le10$ $x\ge0$ $y\ge0$ A) A triangle. B) A quadrilateral. C) A pentagon. D) An equilateral triangle. Show Answer Correct Answer: B) A quadrilateral. 8. Given the relation P on the set E = {a, b, c, d} defined by P = {(a, a), (b, b), (c, c), (d, d), (a, b), (b, a)}, is P an equivalence relation? Why or why not? A) Yes, P is an equivalence relation because it is symmetric. B) No, P is not an equivalence relation because it is not reflexive. C) Yes, P is an equivalence relation because it is reflexive. D) No, P is not an equivalence relation because it is not transitive. Show Answer Correct Answer: D) No, P is not an equivalence relation because it is not transitive. 9. Tentukan nilai y dari $3y-7=2$ A) 1. B) 3. C) 2. D) 4. Show Answer Correct Answer: C) 2. 10. Consider the matrices $A$ $B$ $AB \neq BA$ A) Associative property. B) Distributive property. C) Non-commutative property. D) Commutative property. Show Answer Correct Answer: C) Non-commutative property. 11. What is the objective function? A) P = 2x + 3y. B) P = 6x + 3y. C) P = 24x + 36y. D) P = 18x + 12y. Show Answer Correct Answer: D) P = 18x + 12y. 12. Describe the process of graphing a system of linear inequalities with three or more constraints. A) The process involves graphing each linear inequality separately, identifying overlapping shaded regions, and determining the common region that satisfies all constraints. B) Graphing all linear inequalities simultaneously. C) Ignoring the shaded regions. D) Selecting only one constraint to graph. Show Answer Correct Answer: A) The process involves graphing each linear inequality separately, identifying overlapping shaded regions, and determining the common region that satisfies all constraints. 13. The points where constraints intersect on the boundary of the feasible region are termed as the A) Feasible edges. B) Objective function contour. C) Feasible points. D) Extreme points. Show Answer Correct Answer: D) Extreme points. 14. A constraint of the form x + y $\geq$ 8 represents: A) Below the line. B) Above the line. C) Only the line. D) None of these. Show Answer Correct Answer: B) Above the line. 15. Impact of changes in RHS values of constraints is typically measured by the: A) Reduced cost. B) RHS allowable increase value. C) RHS allowable decrease value. D) Shadow price. Show Answer Correct Answer: D) Shadow price. 16. The slack value for binding constraints is A) Equal to the sum of the optimal points in the solution. B) Always a positive integer. C) Zero. D) A negative integer. Show Answer Correct Answer: C) Zero. 17. Objective function of LPP is A) A constraint. B) Feasible region. C) A function to be optimized. D) An inequality. Show Answer Correct Answer: C) A function to be optimized. 18. Given the objective function z = 3x + 4y, how do you determine the maximum value? A) Evaluate z at the vertices of the feasible region to find the maximum value. B) Set z equal to zero and solve for x and y. C) Calculate the derivative of z to find the maximum value. D) Use the midpoint of the feasible region to estimate the maximum value. Show Answer Correct Answer: A) Evaluate z at the vertices of the feasible region to find the maximum value. 19. Which of the following represents the decision variables in a linear programming model for forest production planning? A) Available land area. B) Labor hours available. C) Number of hectares of each tree species to be harvested. D) Total revenue from timber sales. Show Answer Correct Answer: C) Number of hectares of each tree species to be harvested. 20. What is the best answer we can find in a problem? A) An irrelevant answer. B) The least effective solution. C) The most effective solution. D) A random guess. Show Answer Correct Answer: C) The most effective solution. 21. Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution set of this problem? A) $\left(-\infty, \-21\right)$. B) $\left(-\infty, \-21\right]$. C) $\left(21, \\infty\right)$. D) $\left(-21, \\infty\right)$. Show Answer Correct Answer: B) $\left(-\infty, \-21\right]$. 22. Non-negativity constraint ensures: A) Variables are decimals. B) Variables are always positive or zero. C) Variables are negative. D) Variables are integers. Show Answer Correct Answer: B) Variables are always positive or zero. 23. A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is: A) X1 + x2 + x3 = 24. B) 4x1 + 3x2 + 2x3 = 24. C) X1 = 8, x2 = 8, x3 = 8. D) X1 + x2 + x3 = 24. Show Answer Correct Answer: B) 4x1 + 3x2 + 2x3 = 24. 24. If constraints have a less than equal to sign, ..... variables should be used to apply the Simplex Method. A) Slack. B) Artificial. C) Slack and artificial. D) All are correct. Show Answer Correct Answer: A) Slack. 25. Solve the linear programming problem:Minimize z = x + 2y subject to x + y $\geq$ 5, 2x + y $\geq$ 8, x $\geq$ 0, y $\geq$ 0. A) 6. B) 10. C) 8. D) 4. Show Answer Correct Answer: A) 6. 26. What is the difference between a maximization and a minimization problem? A) Maximization and minimization are the same and yield identical results. B) Maximization seeks to maximize an objective function; minimization seeks to minimize it. C) Maximization is only applicable in linear programming; minimization is not. D) Maximization focuses on minimizing costs; minimization focuses on maximizing profits. Show Answer Correct Answer: B) Maximization seeks to maximize an objective function; minimization seeks to minimize it. 27. What happens if we change a constraint in our problem? A) Changing a constraint has no effect on the feasible region. B) Constraints can only be added, not changed. C) Changing a constraint will always lead to a worse solution. D) Changing a constraint can change the feasible region and the optimal solution. Show Answer Correct Answer: D) Changing a constraint can change the feasible region and the optimal solution. 28. A sketch artist sells on demand portraits and name doodles at the state fair. The artist has a personal maximum of 40 creations per day. With his current paper supply, the artist is equipped to create up to 30 portraits and up to 20 name doodles. The artists profit is $ 10 on each portrait and $ 20 on each name doodle. Let x represent portraits and y represent name doodles. What is the artist's maximum profit? A) 400. B) 500. C) 300. D) 600. Show Answer Correct Answer: D) 600. 29. Corresponding to each dual there exists a primal A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 30. Objective quantity:P = 30x + 50yCorner that maximizes profit:(0, 6)What is the profit? A) 400. B) 300. C) 240. D) 280. Show Answer Correct Answer: B) 300. 31. Find the inverse of the matrix [[0, 1], [1, 0]]. A) [[1, 1], [1, 1]]. B) [[0, 1], [1, 0]]. C) [[1, 0], [0, 1]]. D) [[0, 0], [0, 0]]. Show Answer Correct Answer: B) [[0, 1], [1, 0]]. 32. The common region represented by the inequalities $x+2y\ge3$ $x+4y\ge4$ $3x+y\ge3$ $x\ge0$ $y\ge0$ A) A triangle. B) Unbounded. C) A pentagon. D) A quadrilateral. Show Answer Correct Answer: B) Unbounded. 33. What are the outcomes of completing Unit-10 on Teaching introduction to Linear Programming? A) Identify effective teaching strategies. B) All of the above. C) Analyze constraints and formulate objective functions. D) Make informed decisions based on quantitative analysis. Show Answer Correct Answer: B) All of the above. 34. Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the corner points? A) (0, 0), (3, 5), (6, 0). B) (0, 2), (3.5, 4.5), (6, 2). C) (2, 0), (4, 5), (6, 0). D) (2, 0), (3, 5), (0, 6). Show Answer Correct Answer: B) (0, 2), (3.5, 4.5), (6, 2). 35. When the constraint is compose of only one variable, the form of the line is A) A vertical line. B) A horizontal line. C) A diagonal line. D) None of the above. Show Answer Correct Answer: D) None of the above. 36. What role does the slope of a line play in linear programming? A) The slope only affects the y-intercept of the line. B) The slope determines the color of the line in a graph. C) The slope indicates the relationship between variables and helps define constraints in linear programming. D) The slope is irrelevant in linear programming. Show Answer Correct Answer: C) The slope indicates the relationship between variables and helps define constraints in linear programming. 37. How can linear programming be applied in supply chain operations? A) Managing human resources. B) Analyzing market trends. C) Optimizing crop yields. D) Determining the most cost-effective way to transport goods. Show Answer Correct Answer: D) Determining the most cost-effective way to transport goods. 38. Maximize P = 3x + y with the following constraints:$x+y\\le300$ $y\\ge100$ $x\\le150$ A) X = 150, y = 100. B) X = 100, y 150. C) X = 0, y = 100. D) X = 0, y = 300. E) X = 150, y = 150. Show Answer Correct Answer: E) X = 150, y = 150. 39. When it is not possible to find solution in LPP, it is the case of A) Malaria?. B) Infeasible solution. C) Unknown solution. D) Unbounded solution. Show Answer Correct Answer: B) Infeasible solution. 40. The optimal value of the objective function is A) Given by the intersection of inequalities with Y-axis only. B) Given by the corner points of the feasible region. C) Given by the intersection of inequalities with X-axis only. D) Given by the intersection of inequalities with the axes only. Show Answer Correct Answer: B) Given by the corner points of the feasible region. 41. Math symbols representing activity with limitations in an organization. A) OBJECTIVE FUNCTION. B) CONSTRAINTS. C) DECISION VARIABLES. D) PARAMETERS. Show Answer Correct Answer: C) DECISION VARIABLES. 42. 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. What are the variables you need to define? A) X is gas, y is moped. B) X is car, y is mileage. C) X is gas, y is mileage. D) X is car, y is moped. Show Answer Correct Answer: D) X is car, y is moped. 43. Which of the following is true about the optimal investment strategy in portfolio management? A) It is always found at the center of the feasible region of investment options. B) It may occur at any point within the feasible region of investment options. C) It is always found at a corner point of the feasible region of investment options. D) It does not exist for all portfolio management scenarios. Show Answer Correct Answer: C) It is always found at a corner point of the feasible region of investment options. 44. In linear programming, inequalities are used to describe the limits of the problem. These inequalities are called ..... A) Constraints. B) Optimized. C) Objects. D) Functions. Show Answer Correct Answer: A) Constraints. 45. Question 4:Can the feasible region be empty in a linear programming problem? Why or why not? A) No, because feasible regions are always non-empty. B) Yes. C) Yes, because linear programming does not have a feasible region. D) No, because linear programming always has a feasible region. Show Answer Correct Answer: B) Yes. 46. What is the purpose of conducting sensitivity analysis in LP models? A) To optimize decision variables. B) All of the above. C) To visualize geometric relationships. D) To understand the impact of changes on the optimal solution. Show Answer Correct Answer: C) To visualize geometric relationships. 47. A linear programming problem can be both unbounded and infeasible.2. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 48. What does sensitivity analysis in linear programming involve? A) Solving the problem analytically. B) Using only one decision variable. C) Ignoring constraints. D) Visually analyzing changes in coefficients. Show Answer Correct Answer: D) Visually analyzing changes in coefficients. 49. Consider the following linear programming problem:Maximize Z = 12x + 10y Subject to:4x + 3y<=480 2x + 3y<=360 all variables >= 0 Which of the following points (x, y) could be a feasible corner point? A) (40, 48). B) (120, 0). C) (180, 120). D) None of the above. Show Answer Correct Answer: B) (120, 0). 50. A basic solution is said to be degenerated if A) One or more basic variable become zero. B) Greater than zero. C) Equal to one. D) None of above. Show Answer Correct Answer: A) One or more basic variable become zero. 51. The objective function in an LP problem is: A) Always maximized. B) Either maximized or minimized. C) Irrelevant. D) Always minimized. Show Answer Correct Answer: B) Either maximized or minimized. 52. What does 'certainty' mean in the context of linear programming? A) Values are estimated. B) All values are known. C) Values are uncertain. D) Values can change. Show Answer Correct Answer: B) All values are known. 53. What is the first step in formulating a Linear Programming problem? A) Determine the decision variables. B) Identify the constraints. C) Analyze the feasible region. D) Define the objective function. Show Answer Correct Answer: A) Determine the decision variables. 54. The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $ 38. The school took in $ 52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used? A) S + c = 38s + c = 52. B) 3s + 3c = 381s + 2c = 52. C) 1s + 3c = 382s + 3c = 52. D) 3s + 1c = 383s + 2c = 52. Show Answer Correct Answer: D) 3s + 1c = 383s + 2c = 52. 55. The optimal solution to a linear programming problem always occurs: A) Along the objective function. B) Outside the feasible region. C) At a corner (extreme) point of the feasible region. D) At the center of the feasible region. Show Answer Correct Answer: C) At a corner (extreme) point of the feasible region. 56. What is the main objective of teaching linear programming? A) To avoid real-world problem-solving. B) To memorize formulas without understanding their application. C) To help students make informed decisions based on quantitative analysis and optimization. D) To confuse students with complex mathematical concepts. Show Answer Correct Answer: C) To help students make informed decisions based on quantitative analysis and optimization. 57. The FFA Club plans to grow Christmas 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 = x + y. B) P = 1200x + 576y. C) P = 15x + 18y. D) P = 576x + 1200y. Show Answer Correct Answer: C) P = 15x + 18y. 58. A special case when an LP problem has no solution even though all constraints are being satisfied. A) Unboundedness. B) Infeasibility. C) Alternate solutions. D) Redundancy. Show Answer Correct Answer: B) Infeasibility. 59. Which of the following is the first step in formulating a linear programming problem for maximizing profit in a manufacturing business? A) Determine the non-negative restrictions for the production quantities. B) Define the constraints such as resource limitations. C) Construct the objective function to maximize total profit. D) Identify the decision variables such as the quantity of each product to produce. Show Answer Correct Answer: D) Identify the decision variables such as the quantity of each product to produce. 60. When applying the simplex method in optimizing a portfolio, what is the significance of the pivot element? A) It represents the maximum return the portfolio can achieve. B) It determines the direction of movement towards the optimal portfolio mix. C) It is the element that is used to perform row operations to update the optimization tableau. D) It is used to eliminate assets from the portfolio optimization process. Show Answer Correct Answer: C) It is the element that is used to perform row operations to update the optimization tableau. ← 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 7Class 12 Mathematics Chapter 12 Linear Programming Quiz 8 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books