This problem is essentially used for establishing a policy for production within a time period that satisfies certain demand requirements, respecting the manufacturing limits and at a minimal cost. These types of models can be extended to use with several products, however, for this example we will only consider one single product $---$ Road Race Bicycle:

$\backslash$table$[[$Month$,$Max. Production,Demand,Production Cost,Inventory Cost$],[$January$,120,100,60,15],[$February$,120,130,60,15],[$March$,150,160,55,20],[$April$,150,160,55,20],[$May$,150,140,50,20],[$June$,150,140,50,20]]$

We define the following linear optimization model: $($Given: there is an initial inventory of $50$ units.

Company wants to minimize production and inventory cost.