Question

A C E G K SECTION I-Short answers (3 points each) MAKE SURE TO ANSWER QUESTIONS IN DETAILS TO EARN FULL POINTS 1. What does range of optimatility mean? If there is a change in the optimality range, what will happen? 92. What does range of feasibility mean? If there is a change in the feasbility range, what will happen? 0 1 2 14 3. What variables compose the optimal solution? Give an example. 15 16 17 18 19 4. What does the dual value mean? What is another name for the dual value (solver)? 20 21 22 23 24 5. What does slack mean? 25 26 27 28 29 30 31 32 co

Answer 1

Range of optimality: Range of optimality refers to the maximum and the minimum value a study variable can acquire in a given period of time. The range of values should not change the nature of the variable under any circumstances. For example, the supply of products is a variable which is greatly dependent on its demand in the market. Whenever the demand is high, supply acquires a higher value, and whenever the demand is low, supply acquires a lower value.

Range of feasibility: The range of Feasibility is concerned with the span of change in Right Hand Side (RHS) values for the constraints which can vary along with the constant values of shadow or dual prices and variables in a solution which will remain same. Duel prices imply for the increase in the price of optimal solution per unit in the right-hand side. It is the amount that will be changed in objective function due to one unit increase in the Right-Hand Side value of a constraint.

The range of feasibility is determined by the mathematical technique and linear programming method after attaining the optimum in solutions for issues and problems in operations. The identification procedure is known as sensitivity analyses in linear programming. The range of feasibility is bounded by the constraints given and limited resources shown in Right-Hand Side values and eventually, it limits the optimal solution. Theoretically, it is the span from which a feasible solution can emerge or the scope of a feasible solution (feasible solution is any combination which can satisfy the situation along with constraints and limited resources, which further may be the optimal one).

Optimal solution: P maximize f(x) subject to x ∈ X , where f : Rⁿ 7→ R and X is a closed subset of Rⁿ

The optimal solution to an optimization problem is given by the values of the decision variables that attain the maximum (or minimum) value of the objective function over the feasible region. In problem P above, the point x ∗ is an optimal solution to P if x ∗ ∈ X and f(x ∗ ) ≥ f(x) for all x ∈ X. It is possible that there may be more than one optimal solution, indeed, there may be infinitely many

Slack: The amount of scarce resource of capacity that will be unused by a give feasible solution to a linear programming problem.

A slack or surplus value is reported for each of the constraints. The term "slack" applies to less than or equal constraints, and the term "surplus" applies to greater than or equal constraints. If a constraint is binding, then the corresponding slack or surplus value will equal zero. When a less-than-or-equal constraint is not binding, then there is some un-utilized, or slack, resource. The slack value is the amount of the resource, as represented by the less-than-or-equal constraint, that is not being used. When a greater-than-or-equal constraint is not binding, then the surplus is the extra amount over the constraint that is being produced or utilized.

The units of the slack or surplus values are the same as the units of the corresponding constraints.

Dual Value: The change in the value of the objective function per unit increase in the right-hand side of a constraint.

The dual prices are some of the most interesting values in the solution to a linear program. A dual price is reported for each constraint. The dual price is only positive when a constraint is binding.

The dual price gives the improvement in the objective function if the constraint is relaxed by one unit.

In the case of a less-than-or-equal constraint, such as a resource constraint, the dual price gives the value of having one more unit of the resource represented by that constraint. In the case of a greater-than-or-equal constraint, such as a minimum production level constraint, the dual price gives the cost of meeting the last unit of the minimum production target.

The units of the dual prices are the units of the objective function divided by the units of the constraint. Knowing the units of the dual prices can be useful when you are trying to interpret what the dual prices mean.

It is also called as shadow price.