Question

Which of the following is the correct formulation of the linear programming problem ?

• A. Max \(Z=2x_1-x_2\) ;subject to \(x_1+x_2≤10;x_1≤3;x1≥0;x_2≤0 \)
• B. Max \(Z=3x_1+2x_2\) ;subject to \( x_1+2x2≥11;3x_1+x_2≥24;x_1≥0;x1,x_2≤0\)
• C. Min \(Z=x_1+5x_2\) ;subject to \(2x_1+5x_2≤10;x_1+3x_2≤9;x_1,x_2≥0\)
• D. Min \(Z=4x_1+3x_2\) ;subject to \(x_1+9x_2≥8;2x_1+5x_2≤9;x_1≤0,x_2≥0 \)
• E. Max \(Z=2x_1+5x_2\) ;subject to \(4x_1+9x_2≤8;2x_1+3x_2≤9;x_1≥0;x_1,x_2≤0\)

Answer 1

Answer: (E)

By considering all the given options we found the option which is correct formulation for the Linear Programming problem is :

Max \(Z=2x_1+5x_2\) ;subject to \(4x_1+9x_2≤8;2x_1+3x_2≤9;x_1≥0;x_1,x_2≤0\)

let us discuss how:

As in this problem, we want to maximize the objective function \(Z = 2x_1 + 5x_2\) , subject to the given constraints are ;

1. \(4x_1 + 9x_2 ≤ 8\)
2. \(2x_1 + 3x_2 ≤ 9\)
3. \(x_1 ≥ 0\) (non-negativity constraint)
4. \(x_2 ≤ 0 \) (non-positivity constraint)

These constraints define the feasible region, and the objective is to find the values of \(x_1\) and \(x_2\) that maximize \( Z \) within this feasible region.