Modeling.

The decisions seem to be how many of each computer to produce in each period at regular time, how many to produce at overtime, and how much inventory to carry in each period. Let's denote our time periods t = 1,2,3,4. Let be the number of notebooks produced in period t at regular time and be the number of notebooks produced in period t at overtime. Finally, let be the inventory at the end of period t.

Look at the first quarter: how are these variables restricted and related?

Clearly we need and . Now, anything that starts as inventory or is produced in the period must either be used to meet demand or ends up as inventory at the end of period 1. This means:

For period 2, in addition to the upper bounds, we get the constraint

For period 3, we get

and for period 4 (assuming no inventory at the end):

Our objective charges 2000 for each x, 2200 for each y, and 100 for each i: