4. For a linear programming max:=5x,+2r+3 ≤b1 5x2-6x3≤b2 x1,x2,x3≥0 In this model, b1, b 2 are unknown parameters, and the final simplex table is Basic variable E Coefficient of: Right side (2)0 Please determine the parameters in b1, b2 LP model and a, b, c, d, e in final simplex table.(15 Solution: because B-b-1 ob 1110/sb=30,b2=4 105 e=0d=5,B-A2 sob=5,c=10,a=23 5. Consider the transportation problem having the following cost and requirements Destination supply 6 Source 2 2 4 Demand Determine the optimal solution (15 points) Solution: the optimal transportation plan is described in following table: the red words in square blanks are the optimal shipment. The minimum shipping cost is 32 Destination 6 Source 3(2) 3(3) 6. For a linear programming model (15 points)3 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） Solution: because ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = − 10 30 1 1 1 0 2 1 1 b b B b , so b1=30, b2=40 e=0,d=5, ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = − c b B A 5 5 1 1 1 0 2 1 , so b=5,c=-10,a=23 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) Solution: the optimal transportation plan is described in following table: the red words in square blanks are the optimal shipment. The minimum shipping cost is 32. Destination 1 2 3 4 Supply 1 3(3) 7 6 4(2) 5 Source 2 2 4 3(2) 2 2 3 4 3(3) 8 5 3 Demand 3 3 2 2 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