Q1: 1. Which of the following is not a characteristic of linear programming?

• A) Involves maximizing or minimizing a linear objective function
• B) Subject to linear equality and inequality constraints
• C) Always has a unique optimal solution
• D) Involves non-linear objective functions

Q2: 2. A furniture company wants to maximize its profit by producing chairs and tables. Each chair gives a profit of $20 and each table gives a profit of $30. If the company can produce at most 100 units of chairs and tables combined, what is the objective function for this problem?

• A) 20x + 30y
• B) 30x + 20y
• C) 100x + 100y
• D) 200x + 300y

Q3: 3. Which of the following is true about the feasible region in linear programming?

• A) It contains all possible solutions to the problem
• B) It is determined by the objective function
• C) It is the set of all feasible combinations of decision variables
• D) It is always unbounded

Q4: 4. A farmer wants to maximize the crop output from two fields. Field 1 can produce 4 units of crop per acre and Field 2 can produce 6 units of crop per acre. If the farmer has at most 50 acres available for cultivation, what is the objective function for this problem?

• A) 4x + 6y
• B) 6x + 4y
• C) 50x + 50y
• D) 100x + 200y

Q5: 5. Which of the following is not a method to solve linear programming problems?

• A) Graphical method
• B) Simplex method
• C) Branch and bound method
• D) Gradient descent method

Q6: 6. A company produces two products, A and B. Product A requires 3 hours of labor and Product B requires 5 hours of labor. If the company has at most 240 hours of labor available, what is the constraint equation for labor?

• A) 3x + 5y ≤ 240
• B) 5x + 3y ≤ 240
• C) 240x + 240y
• D) 120x + 200y

Q7: 7. In linear programming, the feasible region is defined by

• A) All points that satisfy the constraints
• B) All points that maximize the objective function
• C) All points that minimize the objective function
• D) All points that lie outside the constraints

Q8: 8. A manufacturing company wants to minimize its production costs by using two types of raw materials. If Material X costs $5 per unit and Material Y costs $8 per unit, what is the cost function for this problem?

• A) 5x + 8y
• B) 8x + 5y
• C) 13x + 40y
• D) 40x + 13y

Q9: 9. Which of the following is not a requirement for a problem to be solved using linear programming?

• A) The problem must have a linear objective function
• B) The problem must have linear constraints
• C) The problem must have discrete decision variables
• D) The feasible region must be bounded

Q10: 10. A transportation company wants to minimize its fuel costs for delivering goods to different locations. If the fuel cost per mile is $2, what is the objective function for this problem?

• A) 2x
• B) 2y
• C) 2xy
• D) 2(x + y)

Q11: 11. Which of the following is not a phase in the linear programming process?

• A) Formulating the problem
• B) Solving the problem
• C) Implementing the solution
• D) Ignoring the constraints

Q12: 12. A restaurant wants to maximize its revenue by selling two types of meals. Meal A costs $10 and Meal B costs $15. If the restaurant can sell at most 50 meals in total, what is the constraint equation for this problem?

• A) 10x + 15y ≤ 50
• B) 15x + 10y ≤ 50
• C) 50x + 50y
• D) 100x + 150y

Q13: 13. Which of the following statements is true about the optimal solution in linear programming?

• A) There can be multiple optimal solutions
• B) The optimal solution is always at a corner point of the feasible region
• C) The optimal solution is always at the center of the feasible region
• D) The optimal solution is independent of the objective function

Q14: 14. A company wants to maximize its profit by producing two products, P1 and P2. Each unit of P1 gives a profit of $50 and each unit of P2 gives a profit of $70. If the company can produce at most 200 units of P1 and P2 combined, what is the objective function for this problem?

• A) 50x + 70y
• B) 70x + 50y
• C) 200x + 200y
• D) 400x + 600y

Q15: 15. In linear programming, the term "binding constraint" refers to a constraint that

• A) Does not affect the feasible region
• B) Is not part of the problem
• C) Limits the feasible region
• D) Is not necessary to consider

Q16: 16. A company wants to minimize its packaging costs for two types of products. If each unit of Product X requires 3 units of packaging material and each unit of Product Y requires 5 units of packaging material, what is the cost function for this problem?

• A) 3x + 5y
• B) 5x + 3y
• C) 3x + 3y
• D) 5x + 5y

Q17: 17. Which of the following is a common application of linear programming in real life?

• A) Designing computer games
• B) Planning a balanced diet
• C) Writing novels
• D) Painting a masterpiece

Q18: 18. A company wants to maximize its revenue by selling two types of products, P and Q. Each unit of P sells for $20 and each unit of Q sells for $30. If the company can sell at most 100 units of P and Q combined, what is the objective function for this problem?

• A) 20x + 30y
• B) 30x + 20y
• C) 100x + 100y
• D) 200x + 300y

Q19: 19. Which of the following is not a type of linear programming problem?

• A) Maximization problem
• B) Minimization problem
• C) Unbounded problem
• D) Infeasible problem

Q20: 20. A company wants to minimize its production costs by using two types of resources. If Resource X costs $3 per unit and Resource Y costs $5 per unit, what is the cost function for this problem?

• A) 3x + 5y
• B) 5x + 3y
• C) 8x + 10y
• D) 15x + 25y

Q21: 21. In a linear programming problem, the optimal solution

• A) Is always at a vertex of the feasible region
• B) Is always at the center of the feasible region
• C) Can be anywhere inside the feasible region
• D) Is always at the boundary of the feasible region

Q22: 22. A company wants to maximize its profit by producing two types of products, A and B. Each unit of A gives a profit of $25 and each unit of B gives a profit of $35. If the company can produce at most 150 units of A and B combined, what is the objective function for this problem?

• A) 25x + 35y
• B) 35x + 25y
• C) 150x + 150y
• D) 300x + 450y

Q23: 23. Which of the following is a key step in solving a linear programming problem using the simplex method?

• A) Plotting the feasible region on a graph
• B) Calculating the objective function
• C) Finding the feasible region algebraically
• D) Iteratively improving the solution

Q24: 24. A company wants to minimize its shipping costs for delivering goods to different locations. If the shipping cost per unit distance is $3, what is the cost function for this problem?

• A) 3x
• B) 3y
• C) 3xy
• D) 3(x + y)

Q25: 25. Which of the following is true about the shadow price in linear programming?

• A) It represents the change in the objective function value with a unit increase in the right-hand side of a constraint
• B) It is always negative
• C) It does not provide useful information in decision-making
• D) It is not related to the constraints