Question: Exercise N:2 (LP Formulation) (5 pts.) Al-Manhal company faces a distribution problem. The company owns three selling points and a factory. The factory manufactures building

Exercise N:2 (LP Formulation) (5 pts.) Al-Manhal company faces a distribution

Exercise N:2 (LP Formulation) (5 pts.) Al-Manhal company faces a distribution problem. The company owns three selling points and a factory. The factory manufactures building material with a capacity of 350 tons per week. The storage capacities of the selling points S1, and S2, and S3 are 90 tons, 50 tons, and 85 tons, respectively. Al-Manhal deals with four clients: C1,C2,C3, and C4. The weekly demands from these clients are respectively, 60 tons, 80 tons, 55 tons, and 40 tons. Each of these four clients can purchase material either directly from the factory or from any of its selling points. The following table summarizes the distribution costs in Saudi Riyals (SR.) per ton. For instance, it is worth 6.5SR to ship one ton of material from the factory to store S1 and 10SR to ship from store S2 to client C3. Formulate the LP problem that will help the company managerial to minimize the total distribution cost. Hint: The decision variables to be used in the formulation are: - FSi : number of tons shipped from the factory to store Si(1i3) - FCj : number of tons shipped from the factory to client Cj(1j4) - SCij : number of tons shipped from store Si to client Cj(1i3 and 1j4)

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