Question 3 : A company manufactures n products and wants to plan the production of these in a horizon of T periods. Products can be manufactured in one of the possible factories, so assigning the products to factories must also be resolved. There is a demand equal to die for product j in period t. Each product must be assigned to a single factory over the entire horizon, and there is a fixed cost Fik for assigning product ; to factory k. Let be the unit cost of production of product j in period t at factory and the cost of leaving a unit of product jin inventory in period t at factory k. Furthermore, there exists in each factory k a total production capacity, Ckt, and each unit of product uses ak units of factory capacity k. To solve the production plan, the company uses a model that considers the variables the quantity to be produced from j in period t in factory k as inventory of jint in factory k, binary variables yjk which is worth 1 if product j is assigned to factory k and which is the quantity of j dispatched to satisfy the demand in t from factory k. The model is the following: min t=1=1 km 8.a. {* + 1} + Fiskvik jak Vj = 1 1