Question

consider the following linear program: max 5a 2b s.t. 1a − 2b ≤ 440 2a 3b ≤ 610 6a − 1b ≤ 125 a, b ≥ 0 write the linear program in standard form.

Answer 1

To write the linear program in standard form, we need to convert the objective function and the constraints to standard form. The objective function is already in standard form since it is a maximization problem. To convert the constraints to standard form, we need to rewrite them in the form of inequalities where the right side is non-negative. We can multiply each constraint by -1 and add slack variables to put all variables on the left side of the equations.

Step-by-step explanation:

To write the linear program in standard form, we need to convert the objective function and the constraints to standard form. The objective function is already in standard form since it is a maximization problem. To convert the constraints to standard form, we need to rewrite them in the form of inequalities where the right side is non-negative. Let's rewrite each of the constraints in standard form:

1. 1a - 2b ≤ 440 can be rewritten as 1a - 2b + 0s = 440
2. 2a + 3b ≤ 610 can be rewritten as 2a + 3b + 0s = 610
3. 6a - 1b ≤ 125 can be rewritten as 6a - 1b + 0s = 125

Where s represents a slack variable. To put all the variables on the left side of the equations, we can multiply each constraint by -1. This gives us the final linear program in standard form:

maximize 5a + 2b + 0s

subject to:

-1a + 2b + 0s = -440

-2a - 3b + 0s = -610

-6a + 1b + 0s = -125

a, b, s ≥ 0