MGT 361 Exam 1

Unbounded

If the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints, the problem is said to be unbounded.

Linear functions

Mathematical expressions in which the variables appear in separate terms and are raised to the first power

Feasible region

THe set of all feasible solutions

Slack variable

a variable added to the left hand side of a less than or equal to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resource.

Surplus variable

a variable subtracted form the left hand side of a greater than or equal to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level

A(n) ________ is a feasible solution that results in the largest possible objective function value, z, when maximizing or smallest possible z when minimizing.

optimal solution

Management science and operations research both involve

quantitative approaches to decision making

If a constraint can be removed without affecting the shape of the feasible region, the constraint is said to be

redundant

T/F A slack variable is a variable that represents the difference between the amount f a resource that was available and the actual amount used by a solution

true

T/F If a linear program has an optimal solution, then an extreme point must be optimal

true

T/F In a feasible problem, an equal to constraint cannot be redundant

true

The maximization or minimization of a quantity is the

objective of linear programming

Nonnegativity constraints

A set of constraints that requires all variables to be nonnegative.

Linear Programming Model

A mathematical model with a linear objective function, a set of linear constraints, and nonnegative varibles

Mathematical model

A representation of a problem where the objective and all constraint conditions are described by mathematical expressions

Feasible solution

A solution that satisfies all the constraints

Which of the following statements is NOT true? a feasible solution satisfies all constraints an optimal solution satisfies all constraints an infeasible solution violates all constraints a feasible solution point does not have to lie on the boundary of the feasible region

An infeasible solution violates all constraints

Problem Formulation

The process of translating the verbal statement of a problem into a mathematical statement called the mathematical model

Standard form

a linear program in which all the constraints are written as equalities. The optimal solution of the standard form of a linear program is the same as the optimal solution of the original formulation of the linear program

Decision criteria...

are the ways to evaluate the choices faced by the decision maker

The field of management science...

concentrates on the use of quantitative methods to assist in decision making, approaches decision making rationally with techniques based on the scientific method, and is another name for decision a science and for operations research

If a linear program possesses an optional solution, then a(n) _______ will be optimal.

extreme point

T/F A feasible solution is one that satisfies at least one of the constraints in the problem

false

T/F A redundant constraint lies entirely within the feasible region

false

T/F An infeasible problem is one in which the objection function can be increased to infinity

false

T/F The optimal solution to a mathematical model is always the policy that should be implemented by the company

false

T/F The terms stochastic and deterministic have the same meaning in quantitive approaches to decision making

false

A(n) _______ satisfies all the problem's constraints

feasible solution

A linear program which is over constrained so that no point satisfies all the constraints is said to be

infeasible

Identification and definition of a problem...

is the first step of decision making

______ are linear functions that are restricted to be "less than or equal to", "equal to", or "greater than or equal to" a constant

linear constraints

________ are functions in which each variable appears in a separate term raised to the first power and is multiplied by a constrained (which should be 0).

linear functions

The quantitative analysis approach requires

mathematical expressions for the relationship

A(n) _____ problem is one that seeks to maximize an objective function subject to constraints. If both the objective function and the constraints are linear, the problem is referred to as a ______ problem.

mathematical programming; linear programming

A(n) ________ is one in which there is positive slack or surplus when evaluated at the optimal solution

nonbinding constraint

A linear program in which all the variables are non negative and all the constraints are equalities is said to be in ________

standard form

Decision variables...

tell how much or how many of something to produce, invest, purchase, hire, etc.

Alternative optimal solutions

the case in which more than one solution provides the optimal value for the objective function

The first step in problem solving is

the identification of a difference between the actual and desired state of affairs

T/F A nonbinding constraint, like a binding constraint, helps form the shape (boundaries) of the feasible region

true

T/F A problem formulation that includes a term that is the product of two variables would not be a linear program

true