What is matrix form of the system of linear equation?

Ax=b is A is [mxn] matrix;

x column vector with n entries;

b column vector with m entries

Apply the Frobenius theorem in the solution of the system of linear equation?

-System of linear equations has at least one solution if only if the rank of matrix of system is equal to the rank of augmented matrix of system.

-The rank of matrix is number of linear independent rows(columns) in matrix

-The rank of matrix can be set as number of nonzero rows(columns) in row echelon form of matrix

4. Describe the Gauss-Jordan total elimination

is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix.

System of linear equations: Bx=Iy=y

If B has an inverse, then multiplying on the left bvy B-1 yields.

Goal of the elimination one variable is isolated in each row.

Describe the algorithm of finding the inverse matrix?

-Form an augmented nx2n matrix by writing the [nxn] identity matrix right of A’’

-Performing row operations on the augmented matrix transform A to the identity matrix I.

-The matrix I that we added will be automatically transformed to A-I. If it is impossible to transform A into identity, A is not invertible.

Which are the phrase of the decision making process?

-Intelligence, design, choice, implement

Describe the Anthony’s classification of the decision making. Draw the Anthony’s pyramid?

-Strategic Planning

-Tactical Planning -Operations Control.

Which are typical features of the strategic tactic and operational control. Which are the typically decision in those group?

*. Strategic Planning:

- Is concerned mainly with establishing managerial policies.

-Major capital investments.

-These strategic decisions have long-lasting effect sand requires the consideration of uncertainties and risk attitudes.

-Are resolved at fairy high managerial levels

*. Tactical Planning:

- Effective allocation of resources (production m storage) to satisfy demand and technological requirements, taking into account the costs and revenues associated with operation of the resources available to the firm.

-Medium range time horizon

- Require significant aggregation

*. Operations Control:

-Deal with the day-to-day operational and scheduling decisions

-Typical decisions: The assignment of customer orders in the work shop, inventory accounting and inventory controls activities.

Compare programmed and non programmed decisions?

-Programmed: Are those that occur routinely and repetitively

-Non programmed: Are complex, unique and unstructured

Compare the main kinds of the mathematical models(operational exercise, gaming, simulation, analytical)

a. Operational exercise: Is an inductive learning process, characteristic of empirical research in the nature sciences, in which generalizations are drawn from particular observations of a given phenomenon.

b. Gaming: Provides the responsive mechanism to evaluate the effectiveness of proposed alternatives

c. Simulation: Are similar to gaming models except that all human decision-maker are removed from the modeling process.

d. Analytical: Represented completely in mathematical term, normally by meant of a criterion or objective which we seek to Maximize or Minimize

 

Which are the mian types of variablesin the mathematical model

-Decision variables

-Parameters

-Exogenous variables

-Polocies and Constrains

-Performance Measures

- Intermediate Variables

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