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1. Formulate a model and make the calculation for the problem. A logistics company has a large business of transporting materials fromA1,A2,A3 to various destinations B1,B2,B3 ... ,B6 .Daily supply, Daily demand, unit transportation cost from A1,A2,A3 to B1,B2,B3...,B6 is shown in Table. Table Daily supply, Daily demand, unit transportation cost What is the optimal transportation plan to minimize its total transportation cost? 2. Formulate a model and make the calculation for the problem. A factory is ready to produce three products, A, B, and C, which all consume labor and materials, as shown in the table below: Establish a linear programming model for the production plan of the product that can achieve the maximum profit to obtain the optimal solution. And then make the calculation for the problem. 3. Formulate a model and make the calculation for the problem. On farms 1, 2 and 3, with an area of 200, 400 and 600 hectares respectively, three crops are planned to be grown: rice, soybeans and maize, each requiring a minimum harvest of 3740kg,1300kg and 7600kg respectively. The estimated yields for each of the three crops grown on each plot are shown below. Table Unit yields of the three crops on different arable land (in kg/hm2 ) If the crop sells for $1.1/kg for rice, $1.95/kg for soybeans and $0.95/kg for maize, what is the planting plan to maximize total revenue? 4. Please give a case for the applications of linear programming from your own observation (no less than 500 words)