In a desertification combat project, TEMA (Trkiye Erozyonla Mcadele, Aalandrma ve Doal Varlklar Koruma Vakf) has detected three territories under risk in Karapnar (P), Ereli

In a desertification combat project, TEMA (Türkiye Erozyonla Mücadele, Ağaçlandırma ve Doğal Varlıkları Koruma Vakfı) has detected three territories under risk in Karapınar (P), Ereğli (E) and Karaman (K) that may turn into a desert in the upcoming 20 years. TEMA will plant forest trees on these territories. In a desertification combat project, TEMA generally opens one or more distribution centers (DCs) close to the territories. A typical DC is responsible to keep inventory and make necessary shipments to the assigned territories. After a short analysis, TEMA identified three potential DC locations, Ayrancı (A), Böğeçik (B), and Sazgeçit (S). TEMA wants to decide on the DCs to be opened and the distribution plan from opened DCs to territories. TEMA gathered information about the problem and reported in table below. In this table, the tree requirements of each territory, DC capacities, fixed cost of opening each potential DC and the unit shipment cost of a tree from DCs to the territories are given. 

a) Formulate an open-form mathematical model that can be used to minimize the total cost of TEMA in the project. Do not forget to define decision variables, and present the objective function and each constraint clearly. 

b) Incorporate the following constraint into the model above: If the Ayrancı DC is opened, then the Sazgeçit DC must be opened.

Potential DCs Ayranc (A) Becik (B) Sazgeit (S) Tree requirement (x1000) Table: TEMA Desertification Combat Project Data Unit Shipment Cost (in TL for 1000 trees) Destination Karapnar Ereli (K) (E) 700 500 800 400 300 500 50 40 Karaman (K) 100 600 900 30 Fixed Cost (x1000 TL) 40 35 45 Tree Capacity (x1000) 60 70 60