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.