3D.5.1 Formulating linear programs Quiz: Pearson Edexcel Further Maths, Unit 39

The 20 questions

1. What is the objective function in a linear programming problem?

   • Expression to optimise
   • Constraint limit value
   • Non-negativity condition
   • Feasible region boundary

2. How are constraints in a linear programme mathematically represented?

   • Inequalities or equations
   • Quadratic expressions
   • Non-linear functions
   • Strict equalities only

3. What condition do non-negativity constraints place on decision variables?

   • Strictly positive values
   • Non-negative values
   • Values below zero
   • Integer values only

4. A slack variable is introduced for

   • a less-than-or-equal-to constraint
   • a greater-than-or-equal-to constraint
   • the objective function
   • an equality constraint

5. A surplus variable is introduced for

   • an equality constraint
   • the objective function
   • a greater-than-or-equal-to constraint
   • a less-than-or-equal-to constraint

6. Which type of constraint requires an artificial variable when setting up simplex?

   • Strictly less than
   • Non-negativity condition
   • Greater-than or equal
   • Less-than or equal

7. What is the feasible region of a linear programme?

   • Region outside boundaries
   • Objective function graph
   • Unbounded solution space
   • Region satisfying constraints

8. A factory makes chairs (x) and tables (y), with profit 10x + 15y. Which is the objective?

   • Minimise P = 10x + 15y
   • Maximise 2x + 3y
   • Maximise x + y
   • Maximise P = 10x + 15y

9. Each chair takes 2 hours of labour, each table takes 3 hours, and 60 hours are available. Which constraint models this?

   • 2x - 3y <= 60
   • 2x + 3y <= 60
   • 2x + 3y >= 60
   • 2x + 3y = 60

10. At least twice as many Y as X is required. Which constraint is correct?

    • y >= 2x
    • x >= 2y
    • y <= 2x
    • 2y = x

11. Write 3x + 4y <= 24 in standard form using a slack variable s1.

    • 3x + 4y + s1 = 0
    • 3x + 4y + s1 = 24
    • 3x + 4y - s1 = 24
    • 3x + 4y = 24 + s1

12. Write x + y >= 5 in standard form using a surplus variable s.

    • x + y - s = 5
    • x + y + s = 5
    • x - y - s = 5
    • x + y - s = -5

13. In the tableau for a maximisation with constraints 4x + 5y + 3z <= 16 and 5x + 4y + 6z <= 24, how many slack variables appear?

    • 1
    • 0
    • 3
    • 2

14. Why is the point (4, 4) not feasible for the constraint x + y <= 5?

    • Constraint is satisfied
    • Sum equals 5
    • Sum exceeds 5
    • Variables are negative

15. A bakery must use at most twice as many A as B. Which constraint models this?

    • x <= 2y
    • x >= 2y
    • x = 2y
    • 2x <= y

16. Maximise P = 5x + 4y with machine hours 2x + y <= 10 and labour x + 2y <= 8. What is P at (2, 3)?

    • 18
    • 23
    • 22
    • 26

17. Why are slack variables added to less-than-or-equal constraints?

    • Increase objective value
    • Remove negative variables
    • Convert to equations
    • Eliminate decision variables

18. A diet needs at least 40 units of a nutrient. Food X gives 4 units per kg and food Y gives 8 units per kg. Which constraint is correct?

    • 4x + 8y = 40
    • 4x + 8y >= 40
    • 4x + 8y <= 40
    • 8x + 4y >= 40

19. What operation is performed on a surplus variable in a greater-than-or-equal constraint?

    • Added to LHS
    • Subtracted from LHS
    • Multiplied by negative
    • Added to RHS

20. Which variables are needed to convert a greater-than-or-equal constraint for initial simplex?

    • Slack and surplus
    • Surplus and artificial
    • Slack and artificial
    • Two slack variables

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