We begin the discussion on models
with an unsuccessful model. It will still be useful, however,
as a base for the successful model described on the next page.
A mathematical programming model of the problem is given below
with nonlinear functions representing the profit terms. The
variables *P*, *Q* and *R* correspond
to the number of units of each product manufactured. The four
machine constraints restrict the total time used for production
to no greater than the time available. The bound constraints
restrict the total production to no greater than the market
can absorb.
To linearize this model, we identify three market
segments for each product.
The objective expressed in terms of the new
variables is linear. We repeat the machine constraints in terms
of the original variables.
We must add constraints to link the new variables
with the original variables *P*, *Q* and *R*.
We include simple upper bounds on the new variables
to represent the size of the market segment.
The new model is a linear program with the solution
below. |