After the
handle has been initialized (e.g.,
e04rac has been called),
e04tac may be used to define
${n}_{\mathrm{add}}$ new unconstrained continuous variables to the problem. If
${n}_{\mathrm{now}}$ denotes the current number of variables in the model, the total number of variables will be
$n={n}_{\mathrm{now}}+{n}_{\mathrm{add}}$ and the new variables will be indexed by
${n}_{\mathrm{now}}+1,\dots ,{n}_{\mathrm{now}}+{n}_{\mathrm{add}}$. The objective function or constraints, if already defined in the model, won't be affected as they will be naturally extended as if the new variables were not referred during their definition (e.g., for a linear objective function the coefficients for the new variables would be set to zero). If the new variables should enter any already defined parts of the problem, you should modify them with the appropriate functions from the suite.
See
Section 4.1 in the
E04 Chapter Introduction for more details about the NAG optimization modelling suite.
None.
Not applicable.
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This example demonstrates, using a simple productionplanning problem, how to use the functions of the NAG optimization modelling suite to edit and solve different variants of the problem.
We consider a situation where a factory can manufacture two different chemicals
${A}_{1}$ and
${A}_{2}$. The goal for the factory is to determine the quantities
${x}_{1}$ and
${x}_{2}$ of each chemical to maximize profit under the following circumstances:

•a unit of ${A}_{1}$ weighs $40$kg and a unit of ${A}_{2}$ weighs $80$kg;

•the total daily production cannot exceed $16000$kg to match the transport capabilities;

•the factory generates $$2$ profit for each unit of ${A}_{1}$ and $$4.5$ profit for each unit of ${A}_{2}$;

•both products need to use the same machine as part of their respective processes; a unit of ${A}_{1}$ requires $1.2$ minutes of machine time while a unit of ${A}_{2}$ requires $3$ minutes; the machine can only function for $1500$ minutes daily;

•a unit of ${A}_{1}$ uses $6$ square metres of packing material while a unit of ${A}_{2}$ uses $10$ square metres; $6000$ square metres of packing materials are available each day;

•production of ${A}_{2}$ is limited to $100$ units per day.
Note that since the chemicals are considered fluid, the quantities
${x}_{1}$ and
${x}_{2}$ are not limited to integer values.
We can now formulate the problem as a linear program:
If the factory expands its capabilities and is now capable of producing a new chemical
${A}_{3}$ with:

•a unit of ${A}_{3}$ takes $5$ minutes on the common machine;

•a unit of ${A}_{3}$ takes $12$ square metres of packaging material;

•a unit of ${A}_{3}$ weighs $120$kg;

•a unit of ${A}_{3}$ generates $$7$ profit;

•production of ${A}_{3}$ is limited to $50$ units per day.
The problem becomes:
At a later date, regulation changes require that products
${A}_{2}$ and
${A}_{3}$ follow a rigorous quality assurance test before being sent to market. Now the factory is only able to process a total of 100 units per day which amounts to adding the following constraint to our linear program:
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