A company produces a set of K products at I plants. It then ships these products to J market zones. For k = I ,..., K, i = I, ..., I, and j = I,... 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, Qi = 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