Chapter 2.Solution of Linear Systems AX=B 华南师范大学数学科学学院谢珊玲
Chapter 2. Solution of Linear Systems AX=B 华南师范大学数学科学学院 谢骊玲
Example-Material Selection Manufacturing a product containing Manganese,silicon,and copper Required amounts [15;22;39]Ibs/ton manufactured 3 supplies exist with different concentrations of each ingredient Problem:How much to buy from each supplier? 华南师范大学数学科学学院谢删玲
Example – Material Selection ◼ Manufacturing a product containing Manganese, silicon, and copper Required amounts [15; 22; 39] lbs/ton manufactured 3 supplies exist with different concentrations of each ingredient ◼ Problem: How much to buy from each supplier? 华南师范大学数学科学学院 谢骊玲
Example-Continued X;=amount to buy from supplierj C=amount of ingredient i required per ton of product manufactured a=amount of ingredient i in each ton from supplier j Supplier 1 Supplier 2 Supplier 3 (lb/ton) (lb/ton) (Ib/ton) Manganese 1 3 2 Silicon 2 4 3 Copper 3 4 7 华南师范大学数学科学学院谢骊玲
Example - Continued ◼ Xj = amount to buy from supplier j ◼ Ci = amount of ingredient i required per ton of product manufactured ◼ aij = amount of ingredient i in each ton from supplier j Supplier 1 (lb/ton) Supplier 2 (lb/ton) Supplier 3 (lb/ton) Manganese 1 3 2 Silicon 2 4 3 Copper 3 4 7 华南师范大学数学科学学院 谢骊玲
Example -Cont. Relation among composition from suppliers,the amount needed from each supplier,and the composition of the final product 含4-ca12g X1+3X2+2X3=15 2X1+4X2+3X=22 3X,+4X2+7X3=39 华南师范大学数学科学学院谢骊玲
Example – Cont. ◼ Relation among composition from suppliers, the amount needed from each supplier, and the composition of the final product 1,2,3 3 1 = = = a X C for i i j ij j 3 4 7 39 2 4 3 22 3 2 15 1 2 3 1 2 3 1 2 3 + + = + + = + + = X X X X X X X X X 华南师范大学数学科学学院 谢骊玲
Example-Truss Truss-structure consisting of rigid members interconnected by Joints ■Example B 92 华南师范大学数学科学学院谢卿玲
Example - Truss ◼ Truss – structure consisting of rigid members interconnected by joints ◼ Example g1 g2 f f 8 4 f f5 5 f3 f2 f2 f6 f7 f1 f1 f3 f4 A B C D q f 华南师范大学数学科学学院 谢骊玲