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)

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 2

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.