Question

8. Given the following 2 constraints, which solution is a feasible solution for a maximization problem?

(i) 8x₁ + 3x₂ ≤ 22; (ii) x₁ – x₂ ≤ 5

A) (x₁, x₂ ) = (1, 5)

B) (x₁, x₂ ) = (5, 1)

C) (x₁, x₂) = (2, 1)

D) (x₁, x₂) = (4, 4)

Answer 1

Given 2 constraints:

(i) 8x1 + 3x2 ≤ 22

(ii) x1 – x2 ≤ 5

Using options to find feasible solution

A), (x1, x2) = (1, 5)

equation i = 8*1 + 3* 5 = 23 which is not less than 22, so option is not correct.

B). (x1, x2 ) = (5, 1)

equation i = 8*5 + 3*1 = 43 which is not less than 22, so option is not correct.

C) (x1, x2) = (2, 1)

equation i = 8*2 + 3*1 = 19 which is less than 22

equation ii is 2 - 1 = 1 which is less than 5, Since both the equation are satisfying, this option is correct answer.

D) (x1, x2) = (4, 4)

equation i = 8*4 + 3*4 = 44 which is not less than 22, so option is not correct.

So, Option C is correct answer.