Constraint Equation Specification

Table 9.1 specifies the available quantities of each input and their usage in the production of X and Y. This information is all that is needed to form the constraint equations.

The table shows that 32 units of input A are available in each period. Four units of A are required to produce each unit of X, whereas 2 units of A are necessary to produce 1 unit of Y. Because 4 units of A are required to produce a single unit of X, the total amount of A used to manufacture X can be written as 4QX. Similarly, 2 units of A are required to produce each unit of Y, so 2Qy represents the total quantity of A used to produce product Y. Summing the quantities of A used to produce X and Y provides an expression for the total usage of A. Because this total cannot exceed the 32 units available, the constraint condition for input A is

The constraint for input B is determined in a similar manner. One unit of input B is necessary to produce each unit of either X or Y, so the total amount of B employed is 1QX + 1QY. The maximum quantity of B available in each period is 10 units; thus, the constraint requirement associated with input B is

Finally, the constraint relation for input C affects only the production of Y. Each unit of Y requires an input of 3 units of C, and 21 units of input C are available. Usage of C is given by the expression 3QY, and the relevant constraint equation is

Constraint equations play a major role in solving linear programming problems. One further concept must be introduced, however, before the linear programming problem is completely specified and ready for solution.

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