Question

Which of the following solutions is an infeasible solution for the following problem?

Maximize P = 3x + 15ysubject to 2x + 4y <= 12
5x + 2y <= 10
and x >= 0, y >= 0
a. (x, y) = (2, 0)
b. (x, y) = (0, 3)
c. (x, y) = (1, 2)
d. (x, y) = (1, 3)
c. None of these.

Answer 1

The infeasible solution for the given problem is (x, y) = (1, 3).

Step-by-step explanation:

To determine which of the given solutions is an infeasible solution for the problem, we need to check if each solution satisfies all the constraints. If a solution violates any of the constraints, it is considered infeasible.

Let's check each solution:

• a. (x, y) = (2, 0): Substitute the values in the constraints. 2x + 4y = 2(2) + 4(0) = 4, which is less than or equal to 12. Therefore, this solution is feasible.
• b. (x, y) = (0, 3): Substitute the values in the constraints. 5x + 2y = 5(0) + 2(3) = 6, which is less than or equal to 10. Therefore, this solution is feasible.
• c. (x, y) = (1, 2): Substitute the values in the constraints. 2x + 4y = 2(1) + 4(2) = 10, which is equal to 10. Therefore, this solution is feasible.
• d. (x, y) = (1, 3): Substitute the values in the constraints. 2x + 4y = 2(1) + 4(3) = 14, which is greater than 12. Therefore, this solution violates the constraint 2x + 4y ≤ 12 and is an infeasible solution.

Therefore, the correct answer is d. (x, y) = (1, 3).