Since the late 1940s linear programming models have been used for many different purposes.
Airline companies apply these models to optimize their use of planes and staff. NASA has been
using them for many years to optimize their use of limited resources. Oil companies use them to
optimize their refinery operations. Small and medium-sized businesses use linear programming to
solve a huge variety of problems often involving resource allocation. In my study a typical
product-mix problem in a manufacturing system producing two products (each product consists of
two sub-assemblies) is solved for its optimal solution through the use of the latest versions
of MATLAB having the command simlp which is very much like linprog. As analysts we try to
find a good enough solution for the decision maker to make a final decision. Our attempt is to
give the mathematical description of the product-mix optimization problem and bring the problem
into a form ready to call MATLAB s simlp command. The objective of this study is to find the
best product mix that maximizes profit. The graph obtained using MATLAB commands give the
shaded area enclosed by the constraints called the feasible region which is the set of points
satisfying all the constraints. To find the optimal solution we look at the lines of equal
profit to find the corner of the feasible region which yield the highest profit. This corner
can be found out at the farthest line of equal profit which still touches the feasible region.
The most critical part is the sensitivity analysis using Excel Solver and Parametric Analysis
using computer software which allows us to study the effect on optimal solution due to
discrete and continuous change in parameters of the LP model including to identify bottlenecks.
We have examined other options like product outsourcing one-time cost cross training of one
operator manufacturing of hypothetical third product on under-utilized machines and optimal
sequencing of jobs on machines.
