A company produces a set of K products at I plants. It then ships these products to J market zones. For k = 1 ..., K, i =1, ..., I, and j = 1, ..., J, the following data is given: vik = variable cost of producing one unit of product k at plant i Cijk = cost of shipping 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 that can be produced at plant i mik= minimal quantity of product k produced at plant I, if plant i produces a nonzero quantity qik= capacity of plant i used to produce one unit of product k Ql = capacity of plant i djk = demand for product k at market zone j Formulate the problem of minimizing the total cost of production and transportation, while satisfying all appropriate constraints. A company produces a set of K products at I plants. It then ships these products to J market zones. For k = 1 ..., K, i =1, ..., I, and j = 1, ..., J, the following data is given: vik = variable cost of producing one unit of product k at plant i Cijk = cost of shipping 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 that can be produced at plant i mik= minimal quantity of product k produced at plant I, if plant i produces a nonzero quantity qik= capacity of plant i used to produce one unit of product k Ql = capacity of plant i djk = demand for product k at market zone j Formulate the problem of minimizing the total cost of production and transportation, while satisfying all appropriate constraints