Question

Maximize 5x+2y

x+y≤50
3x+y≥90
Y=10X,y≥0​
Convert an LP model into standard form.

Answer 1

To convert the given LP model into standard form, rewrite the inequalities as equalities and add slack variables if necessary. Maximize the objective function and write each constraint as an equation, considering non-negativity constraints.

Step-by-step explanation:

To convert the given LP model into standard form, we need to rewrite the inequalities as equalities and add slack variables if necessary. Here are the steps:

1. Maximize: Rewrite the objective function as an equation by introducing a new variable z. The equation becomes: z = 5x + 2yx + y.
2. Inequality Constraints: Write each inequality constraint as an equation by introducing slack variables. For example, the constraint 5x + 2yx + y ≤ 50 becomes: 5x + 2yx + y + s1 = 50, where s1 is the slack variable.
3. Equality Constraints: Write each equality constraint as an equation. For example, the constraint 3x + y ≥ 90 becomes: 3x + y - s2 = 90, where s2 is the slack variable.
4. Non-negativity Constraints: Add non-negativity constraints for each variable. For example, y ≥ 0 becomes: y + s3 = 0, where s3 is the slack variable.

Putting all the equations together, the LP model in standard form is:

Maximize: z = 5x + 2yx + y

Subject to:

5x + 2yx + y + s1 = 50

3x + y - s2 = 90

y + s3 = 0

x, y, s1, s2, s3 ≥ 0