There are many problems that might be posed regarding the
PQ situation, but we choose the problem of allocating the
times available on the machines to the manufacture of the
two products. The decisions involve the amounts of the two
products.

The objective is to maximize profit. From the figure we see
that the profit per unit of product is its unit revenue less
the raw material cost per unit. For P the unit profit is $45
and for Q it is $60. The objective is a linear expression
of the amounts produced.

The constraints specify that the amounts of time required
on each machine must not exceed the amount available. The
amount of time required of a machine is a linear function
of the production amounts.

*Machine Time Constraints*

Finally, we require that the amounts manufactured not exceed
the demand determined by the markets for the products. We
include the nonnegativity requirement with the market constraints.

*Market Constraints*

The linear model is complete. This simple case illustrates
the required parts of the model. First we provide a word definition
of each of the variables of the problem. Next we show the
objective criterion with which alternatives are to be compared.
Then we list the constraints that must be satisfed by a feasible
solution. Each set of constraints should be named to describe
the purpose of the constraint.