The proper definition of the decision variables is an essential first step in the development of the
model. Once done, the task of constructing the objective function and the constraints becomes
more straightforward.
For the Reddy Mikks problem, we need to determine the daily amounts to be produced of
exterior and interior paints. Thus the variables of the model are defined as
Xl = Tons produced daily of exterior paint
X2 = Tons produced daily of interior paint
To construct the objective function, note that the company wants to maximize (i.e., increase
as much as possible) the total daily profit of both paints. Given that the profits per ton of exterior
and interior paints are 5 and 4 (thousand) dollars, respectively, it follows that
Total profit from exterior paint = 5xl (thousand) dollars
Total profit from interior paint = 4X2 (thousand) dollars
Letting z represent the total daily profit (in thousands of dollars), the objective of the company
is