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Quiz

Year 3: Systems of linear inequalities in two unknowns

10 questions with solutions for year 3: linear inequalities, systems of inequalities, maximum and minimum values (linear programming) – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. Is the point (0, 0) a solution of x + y ≤ 3?

2. Is (0, 0) a solution of the system 4x + y ≥ 3, x − 7y ≤ 3?

3. Minimum value of z = 7x + 6y if 5x + 2y ≥ 16, 3x + 7y ≥ 27, x ≥ 0, y ≥ 0

4. Maximum value of z = 6x + 3y if x + y ≤ 6, 9x + 2y ≤ 27, y ≤ 5, x ≥ 0, y ≥ 0

5. Minimum value of z = 3x₁ + 8x₂ if 4x₁ − 5x₂ ≥ 50, −x₁ + 2x₂ ≥ 4, x₁ + x₂ ≤ 80, x₁, x₂ ≥ 0

6. Maximum value of z = 5x + 7y if 2x + 3y ≥ 6, 3x − y ≤ 15, −x + y ≤ 4, 2x + 5y ≤ 27, x ≥ 0, y ≥ 0

7. Minimum value of z = 5x + 7y if 2x + 3y ≥ 6, 3x − y ≤ 15, −x + y ≤ 4, 2x + 5y ≤ 27, x ≥ 0, y ≥ 0

8. Maximum value of z = x + 3y if 3x + y ≥ 45, x + 2y ≥ 50, x + y ≤ 35, x ≥ 0, y ≥ 0

9. A jeweller makes at most 24 bracelets and necklaces a day; a bracelet takes 1 hour, a necklace 1/2 hour, and the shop works 16 hours. The profit is 2 euros a bracelet and 1 euro a necklace. What is the maximum profit (euros)?

10. A fish pond: a carp needs 2 units of food I and 4 of food II, a trout 5 of I and 2 of II; there are 800 units of each. What is the most fish the pond can hold?