WRITE THE MATHEMATICAL MODEL OF THE PROBLEM, SOLVE IT USING LINDO/LINGO

Example: Two-stage distribution problem: RIFIN Company has recently developed a new method of manufacturing a type of chemical The method involves refining a certain raw material that can be obtained from four overseas suppliers, A, B, C, and D, who have access to the four ports at Vancouver, Boston, Miami, and San Francisco, respectively. RIFIN wants to determine the bcation for plants that will refine the material Once refined, the chemical will be transported via trucks to five outlets located in Dallas, Phoenix, Portland, Montreal, and Orlando After an initial study, the choice of location for RIFIN's refineries has been marrowed down to Denver, Atlanta, and Pittsburgh. Assume that one unit of the raw material is required to make one unt of the chemical The amount of raw material that can be obtained from suppliers A, B, C, and D and the amount of chemical required at the five outlets are given in the folowing table (a). The cost of transporting the raw material from each port to each potential refinery and the cost of trucking the chemical to outlets are provided in tables (b) and (c), respectively. Determine the bcations of RIFIN's refining plants, the capacities at these plants, and the distribution pattern for the raw material and processed chemical (a) Supply and demand for four sources and five outlets Demand Raw Material Source A B D Supply 1000 800 800 700 900 800 Outlet Dallas Phoenix Portland Montreal Orlando 600 500 500 Atlanta Pittsburgh (b) Inland raw material transportation cost To Derver From Vancouver 4 Boston 8 Miami 12 San Francisco 11 13 NOUS 9 5 9 12 2 11 Phoenix Portland Montreal Orlando (c) Chemical trucking cost To Dallas From Denver 28 Atlanta 10 Pittsburgh 18 26 22 21 12 23 23 30 29 18 30 8 21