Unit 1 : Infeasibility

If the objective function, f(x, y) = 30x + 32y, needs to be minimized, which of the following is the optimal solution?

(3, 5) OR (6,3) OR (5, 3)

How many constraint(s) can contradict the others within a linear programming model having around 100 constraints to have a feasible region?

0

1. Which of the following is true of the system of constraints, 7x + 9y ≤ 65; x ≥ 0; y ≥ 8? 2. Which of the following is true of the system of constraints, 7x + 9y ≤ 65; y ≥ 0; x ≥ 8?

1. The graph is an infeasible region. OR At least one of the contradictory constraints must be modified. OR There is a contradiction among the constraints. OR It results in no solution. 2. The graph gives a feasible region OR The constraints produce an optimal solution OR It results in no solution OR The constraint y ≥ 8 contradicts another constraint OR There are no contradictions among the constraints.

You are in the business of making tables and chairs. The profit on each chair is $60 and on each table is $70. It takes 1.5 hours to make a chair and 2 hours for a table. The number of chairs should be at least 30 and the number of tables should be at most 40. 1. Identify the corners of the feasible region for the following problem. 2. What should be the lowest value for the right-hand side of a labor constraint added to the following problem to minimally have a bounded feasible region? 3. What constraint should be added to minimally have a bounded feasible region? 4. What is the optimal solution for the profit for the following problem? 5. What would the lowest possible profit be if a labor constraint added to the following problem to close the unbounded feasible region to a closed feasible region?

1. There are not corners to the right side of the region OR This is an unbounded feasible region 2. 45 hours 3. Time OR Labor Constraint 4. Unknown OR The value of objective function increases indefinitely without reaching the maximum OR The value of objective function increases indefinitely without reaching the maximum 5. $1,800

You are in the business of making mug and bowls. The profit on each mug is $6 and on each bowl is $4. It takes 8 minutes to make a mug and 6 minutes for a bowl. The number of mugs should be at least 40 and the number of bowl should be at least 50. You have a total of 4 hours of labor. 1. Which of the constraints violates the linear programming model rules? 2. What should the maximum required number of mugs and bowls be at most to have a feasible region? 3. Identify the feasible region for the following problem.

1. Time constraint for the required number of bowls Time constraint for the required number of mugs 2. 30 mugs OR 40 bowls 3. Infeasible OR There is no feasible region

How many different regions are you dealing with in an infeasible linear programming model?

At least two

Which of the following is true about the solution to the system of constraints in a linear programming model?

Finding it is a key step in the linear programming process. It is a common area that satisfies each of the constraints. It gets more difficult to find as the number of constraints increases.

The constraints for a given linear programming model are as follows: 4g + 5w ≤ 100 w ≤ 15 g ≥ 30 w ≥ 0 Where, g is the number of gizmos produced w is the number of whatsits produced Which of the following is true?

The graph of the system of constraints results in an infeasible region. There is a contradiction between two of the constraints.

Which of the following is true if there is an infeasible region?

The model has no optimal solution. It happens when a common overlapping region that satisfies all constraints does not exist. At least one of the contradictory constraints must be modified. It means the problem is unsolvable.

Which of the following is true of a maximization problem?

The objective function needs to be maximized. The vertex that yields the largest value in the objective function is the solution. The optimal solution is usually on the node farthest from the origin.

When a complicated linear programming model is used to find the optimal solution to a problem, it is important that the constraints are

realistic & reasonable

When a linear programming model has an infeasible region,

the contradictory constraint must be modified

Finding the feasible region gets more difficult when

the number of constraints increases

Which of the following constraints does not contradict the constraint 10x + 15y ≤ 300?

x ≥ 0 x ≥ 29 y ≥ 19

The constraint that contradicts 36x + 40y ≤ 360 is

x ≥ 12

Which of the following constraints contradicts the constraint 6x + 8y ≤ 48?

x ≥ 9 y ≥ 7 y ≥ 8 x ≥ 10