But this is equivalent to
D1(O11 - R1 + Δ) + . . . + D6[(2 - b1)(1 - a1)O21 - R1 + Δ] ≤ 0
D1(O11 - R1) + . . . + D6[(1 - b1)(1 - a1)O21 - R1] + D + ̄Δ ≤ 0
Z ≤ D + ̄Δ
Thus, if we guarantee constant total volume, a concentration constraint can be varied simply by varying the right-hand side.
A variety of indirect influences on residuals generation and discharge may be studied by manipulation of values of the objective function, the right-hand side, or the matrix of coefficients itself. Thus, in the objective function, any of the price or cost figures may, in principle, be altered and the effects observed, though in practice we may be interested only in the price of a key input (such as coal to a thermal-electric generating plant), a particularly important product (such as motor gasoline from a petroleum refinery), or of an actual or potential by-product (such as sulfur from the petroleum refinery). On the right-hand side, one may change input availabilities and output quantity requirements. Finally, advances in production or residuals-handling technology can be reflected by changing coefficients within the A-matrix itself. Such changes may take the form of introducing entire new columns to represent possible new processes. Another alternative is to change one or two coefficients within existing columns to reflect progress in a subprocess of a largely unchanged overall process.
Flow Diagrams for Bleached Kraft Paper Production