The production planning problem that we study here is to determine the start of production in a given period with the number of units (or parts) to be produced. Suppose we have 6 weeks with customer demands of 100, 200, 250, 225, 300, and 125 units for weeks 1-6, respectively. The capacity of the weekly production is assumed to be infinite. Production can be started on Monday morning and must be stopped on Friday evening of each week. It costs $ 1,000 to start production each week * and each unit manufactured costs $ 20, $ 25, $ 15, $ 10, $ 20 and $ 30, respectively for weeks 1 through 6 **. It is possible to produce more than weekly demand and store the surplus from week to week with a storage cost of $ 2 per part. Provide a mathematical optimization model that makes it possible to find a production plan in order to minimize the costs mentioned above. * If production is not started in week d, then the cost of starting production is zero. ** Example: if we decide to produce 100 units in week 1, it costs us: 

1000$+20$*100.