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 through 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.