From this, all the names needed can be formed. For example, quantity
demanded of commodity "C" in region 2 is "XDC2"; quantity traded of com-
modity C from region 1 to region 2 is XTC12.
 The expanded LCP tableau for the problem has the form shown in
 Figure 1. The rows here are expressed as ">" greater than or equal to
 constraints. The first three rows express the requirement that the total
 amount supplied to each region (including domestic supply and net inflows
 from trade) is greater than or equal to the quantity demanded in that
 region. The second set of 3 rows express the relationship that the quantity
 produced in each region is at least as great as the amount supplied to
 all regions. These rows comprise the "A matrix". The next six rows are
 the demand and supply functions. Each of these rows will normally hold
 with strict equality as the complementarity conditions assure this as
 long as positive quantities are produced and demanded.
 The final nine rows, along with their complementarity conditions,
 assure that for each trade flow the associated demand and supply prices
 will differ by no more than the transport cost for that particular flow*
 In summary, the whole matrix describes an economic equilibrium or market
 clearing condition for the commodity sector with which we are concerned.
 The input for this particular problem is shown in Figure 2. The
reader should note the difference between the matrix tableau and the
original economic data with regard to the signs (- or +) attached to Q-
matrix and C-vector (OBJ) values. There are two reasons for this
difference. First of all, the LCRAND and RANDQP work in a tableau
expressed in terms of less than or equal to constraints. The second reason
lies in that a QP problem may be defined with c'x 1/2x'Qx as the objec-
tive function or as c'x + 1/2x'Qx. LCRAND and RANDQP use the latter.
Confusion can be avoided by closely abiding by the following rules:
1) For demand functions, insert both slope and intercept coefficients with
 the opposite signs from what they actually have.
2) Supply function coefficients are inserted with the same signs which
 they actually have.
3) All cost data is inserted with a positive sign.
4) All profit data is inserted with a negative sign.
Inspection of our sample input problem should reveal that these rules
have been followed.