defines the printed output data set. Card 4 defines the punched output data set. Card 5 introduces the user specified input data set which is coming from cards and immediately follows. The section including cards 6-14 is the input file prepared by the user which directs LCRAND as to what actions are to be performed and what data to use in constructing the problem matrix. This input file is composed of control cards and data cards. The control cards tell the program to carry out certain actions and alert the program about what type of data is to follow. Data cards describe the problem itself. The BEGIN card is a control card which indicates the beginning of a problem and causes a set of program parameters to be initialized. The ROWS card indicates that a set of data cards follow which will define the rows of the problem. The END card signals the end of the row data cards. The MATRIX card indicates that the coefficient data cards for the problem matrix are to follow. The next END card signals the end of the matrix data cards. The RHS card indicates that right hand coefficient data cards are to follow. END again has the same function. The SOLVE statement calls the solution algorithm which solves the problem and prints out the solution results. The EXIT statement causes LCRAUD to terminate and the /* card signals the end of the user input deck. 3.2 Input Format 3.2.1 Control cards--All control cards must begin in column 1. 3.2.2 Row data cards--Each row data card defines a row in the A matrix of the problem to be solved. The name of the row is punched in columns 13 to 18 (left-justified with no embedded blanks). The name is made up of any combination of alphanumeric symbols with a maximum of 6 characters per name. The row type is punched as a single character in column 12 according to the following code. $ indicates that this row is actually the c-vector of our problem. This is considered to be a non-constrained row and is the linear part of the objective function for a QP (or LP) problem (corres- ponds to N in the MPS system). See the following sample card.