# Ajax Paper Company Production Schedule

TomSym implementation of GAMS Example (AJAX,SEQ=60)

This sample model is taken from the cybernet pds/apex sample library of models. A paper manufacturer can produce four different types of paper on three different machines. Given a fixed demand schedule the objective is to find a production plan that maximizes monthly profits.

CDC, PDS/APEX Sample Model Library, 1977. Control Data Corporation

```% m: machines at mills (machine 1, machine 2, machine 3)
%
% g: paper grades (20-bond-wt, 25-bond-wt, c-bond-ext, tissue-wrp)

toms 3x1 m
toms 4x1 g

% Matrix prate(g,m) production rate (tons per hour)
prate = [53        52         49;
51        49         44;
52        45         47;
42        44         40];

% Matrix pcost(g,m) production cost (\$ per ton)
pcost = [76        75        73;
82        80        78;
96        95        92;
72        71        70];

demand = [30000; 20000; 12000; 8000];
price = [77;81;99;105];

% Available machine time
avail = [672; 600; 480];

% Production (tons per month)
toms 4x3 outp

% Variable are positive
cbnd = {outp >= 0};

% Machine capacity (hours per month)
eq1 = {sum(outp./prate,1) <= avail'};

% Demand (tons per month)
eq2 = {sum(outp,2) == demand};

% Profit definition (\$ per month)
profit = sum(sum(demand.*price)) - sum(sum(pcost.*outp));

solution = ezsolve(-profit,{cbnd, eq1, eq2});
```
```Problem type appears to be: lp
===== * * * =================================================================== * * *
TOMLAB - Tomlab Optimization Inc. Development license  999001. Valid to 2010-02-05
=====================================================================================
Problem: ---  1:                                f_k -441003.595310464500000000
sum(|constr|)      0.000000000000000121
f(x_k) + sum(|constr|)-441003.595310464500000000
f(x_0)      0.000000000000000000

Solver: CPLEX.  EXIT=0.  INFORM=1.
CPLEX Dual Simplex LP solver
Optimal solution found

FuncEv    8 Iter    8
```