China Steel has received annual orders from four countries (France, Germany, Italy and Japan) for two different types of steels it produces: high-grade and low-grade. These steels are produced at its two mills, located in Beijing and Shanghai, using iron ores supplied by two mining companies (Lanzhou Minerals and Chengdu Mines). The management of China Steel needs an overall annual purchase/production/distribution plan to minimize total costs. Various departments have collected the necessary data regarding the sales commitment, ore availability and cost, production characteristics, and distribution costs of ore and finished steel. China Steel can obtain up to 10,000 tons of Grade-A iron ore from Lanzhou Minerals and up to 20,000 tons of Grade-B iron ore from Chengdu Mines. China Steel can specify how much of each ore is to be shipped to each of its two steel mills. The associated purchase cost and shipping charge per ton are given in Table 1. Table 1: Ore purchase and shipping costs ($/ton) Shipping cost to Purchase cost Beijing Shanghai Lanzhou Minerals 650 50 65 Chengdu Mines 550 70 85 Each of China Steel's two mills can produce high-grade and low-grade steel. High-grade steel requires blending Grade-A and Grade-B iron ore in a ratio of 1 to 2. Low-grade steel requires a ratio of 1 to 3. Thus, producing one ton of high-grade steel requires 1/3 ton of Grade-A iron ore and 2/3 ton of Grade-B iron ore, and producing one ton of low-grade steel requires 1/4 ton of Grade-A iron ore and 4 ton of Grade-B iron ore. The Shanghai mill can process up to 15,000 tons of iron ore, and the Beijing mill can handle at most 7,000 tons. The mill at Beijing is a modern facility and has a lower processing cost per ton of steel produced than does the facility at Shanghai, as indicated in Table 2. Table 2: Processing costs ($/ton) High-grade steel Low-grade steel Beijing 160 Shanghai 195 135 160 The finished steel is shipped to France, Germany, Italy, and Japan. The International Sales Division of China Steel has received orders for each type of steel. Annual demands and unit shipping costs of steel are given in Table 3. Table 3: Annual demands and unit shipping costs of steel Demand Shipping cost (S/ton) from Country Steel type (tons) Beijing Shanghai France High-grade 4000 550 575 Low-grade 2000 500 550 Germany High-grade 2000 700 750 Low-grade 1000 650 725 Italy High-grade 2000 650 675 Low-grade 1000 625 635 Japan High-grade Low-grade 1500 500 400 450 400 425 1 As Manager of the Logistics Group of China Steel, you have been asked to make recommendations on the purchasing, processing, and shipping functions with the objective of minimizing the total annual cost. 1. Formulate a linear programming model for the problem. 2. Solve the linear programming model using Matlab or Excell. 3. Make your recommendations based on the solution