Develop a mathematical model for the transshipment problem , and 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 location 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 narrowed down to Denver, Atlanta, and Pittsburgh. Assume that one unit of the raw material is required to make one unit 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 following 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 locations of RIFIN's refining plants, the capacities at these plants, and the distribution pattem for the raw material and processed chemical (a) Supply and demand for four sources and five outlets Raw Material Supply Outlet Demand 1000 Dallas 900 Phoenix Portland Montreal Orlando Source A B 800 800 800 600 500 500 D 700 (b) Inland raw material transportation cost Denver Adanta Pittsburgh From Vancouver Boston Miami San Francisco 4 8 12 11 13 8 2 11 ama 12 (c) Chemical trucking cost Dallas Phoenix Portland Montreal Orlando From Denver Atlanta Pittsburgh 28 10 18 26 22 21 12 23 23 30 29 18 30 8 21