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Q10: A company produces a set of K products at I plants. It then ships these products to J market zones. For k=1,,K,i1,,I and j11,,J, the following data are given: vik= variable cost of producing one unit of product k at plant i cijk= cost of shi pping one unit of product k from plant i to zone j fik= fixed cost associated with producing product k at plant i Mik= maximal quantity of product k produced at plant i mik= minimal quantity of product k that can be produced at plant i, if plant i produces a nonzero quantity qik= capacity of plant i used to produce one unit of product k Qi= capacity of plant i djk= demand for product k at market zone j a) Formulate the problem of minimizing the total cost of production and transportation that the company is facing, as a mixed integer linear optimization problem. Indicate how your model can incorporate the following additional constraints: b) No plant may produce more than K1 products. c) Every product can be produced in at most I1 plants. d) For a particular product k0, plant 3 must produce it if neither plant 1 nor plant 2 produce it. e) E ach market zone must be sourced by exactly one plant for all products. Q10: A company produces a set of K products at I plants. It then ships these products to J market zones. For k=1,,K,i1,,I and j11,,J, the following data are given: vik= variable cost of producing one unit of product k at plant i cijk= cost of shi pping one unit of product k from plant i to zone j fik= fixed cost associated with producing product k at plant i Mik= maximal quantity of product k produced at plant i mik= minimal quantity of product k that can be produced at plant i, if plant i produces a nonzero quantity qik= capacity of plant i used to produce one unit of product k Qi= capacity of plant i djk= demand for product k at market zone j a) Formulate the problem of minimizing the total cost of production and transportation that the company is facing, as a mixed integer linear optimization problem. Indicate how your model can incorporate the following additional constraints: b) No plant may produce more than K1 products. c) Every product can be produced in at most I1 plants. d) For a particular product k0, plant 3 must produce it if neither plant 1 nor plant 2 produce it. e) E ach market zone must be sourced by exactly one plant for all products

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