Machine Type Available Time(in Machine Hours per Week) Milling machine 500 350 Grinder The number of machine hours required for each unit of the respective products is as Machine type Product Product 2 Product Milling machi Lathe 4 0 The sales department indicates that the sales potential for products I and 2 exceed the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1, 2 and 3 the objective is to determine how much of each product the firm should produce to maximize profit Formulate a li model for this probler 4. For a linear programming x1+5x2+2x3≤b ≤b2 x3≥0 In this model, bi, b2 are unknown parameters, and the final simplex table is Basic variable E Coefficient of X3 X4 s Right side (1)0 abc Please determine the parameters in b1, b2 LP model and a, b, c, d, e in final simplex table.(15 5. Consider the transportation problem having the following cost and requirements table Destination supply 6 Source 4 44252 Demand Determine the optimal solution (15 points) 6. For a linear programming model (15 points)2 Machine Type Available Time (in Machine Hours per Week) Milling machine Lathe Grinder 500 350 150 The number of machine hours required for each unit of the respective products is as follows: Machine Type Product 1 Product 2 Product 3 Milling machine Lathe Grinder 9 5 3 3 4 0 5 0 2 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1,2 and 3. the objective is to determine how much of each product the firm should produce to maximize profit. Formulate a linear programming model for this problem. (10 points) 4. For a linear programming In this model, b1,b2 are unknown parameters，and the final simplex table is： Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 a 7 d e 150 X1 (1) 0 1 b 2 1 0 30 X5 (2) 0 0 c -8 -1 1 10 Please determine the parameters in b1,b2 LP model and a, b, c, d, e in final simplex table。（15 points） 5. Consider the transportation problem having the following cost and requirements table: Destination 1 2 3 4 Supply 1 3 7 6 4 5 Source 2 2 4 3 2 2 3 4 3 8 5 3 Demand 3 3 2 2 Determine the optimal solution. (15 points) 6. For a linear programming model (15 points) ⎪ ⎩ ⎪ ⎨ ⎧ ≥ − − ≤ + + ≤ = + + 0 5 6 5 2 5 2 3 1 2 3 1 2 3 2 1 2 3 1 1 2 3 x x x x x x b x x x b x x x , , s.t. max z