管理數學 Chapter 2 System of linear Equations b
1 管理數學 Chapter 2: System of Linear Equations XX. XX, XXX by XXXX
Agenda Linear Systems as Mathematical models Linear Systems Having One or no solutions Linear Systems having Many Solutions
2 Agenda Linear Systems as Mathematical Models Linear Systems Having One or No Solutions Linear Systems Having Many Solutions
Linear <- Line a,X+ a2 y=b or 日AX+日2Xtan,X nn b
3 Linear <-- Line a1 x + a2 y = b or a1 x1 + a2 x2 +....+ an xn = b
Which one is linear 2X+3y=4 2+y2= 7-X2+X 3 =6 z=5-3X+y/2 sinⅹ+ey=1 =2 7X1+3X2+9/X2+2X4=1 X1+2X2+3x3+…+nXn=1
4 2x + 3y = 4 x 2 + y 2 = 1 x1 - x2 + x3 - x4 = 6 z = 5 - 3x + y/2 sin x + e y = 1 xy = 2 7x1 + 3x2 + 9/x3 + 2x4 = 1 x1 + 2x2 + 3x3 +....+ nxn = 1 Which one is linear?
Example 1 A firm produces bargain and deluxe TV sets by buying the components, assembling them, and testing the sets before shipping
5 Example 1 A firm produces bargain and deluxe TV sets by buying the components, assembling them, and testing the sets before shipping
Resources The bargain set requires 3 hours to assemble and 1 hour to test. The deluxe set requires 4 hours to assemble and 2 hours to test. the firm has 390 hours for assembly and 170 hours for testing each week
6 Resources The bargain set requires 3 hours to assemble and 1 hour to test. The deluxe set requires 4 hours to assemble and 2 hours to test. The firm has 390 hours for assembly and 170 hours for testing each week
Question Use a system of linear equations to model the number of each type of TV set that the company can produce each week while using all of its available labor
7 Question Use a system of linear equations to model the number of each type of TV set that the company can produce each week while using all of its available labor
Problem formulation Define decision variables (unit of scale) Detine the linear relation between variables( write the linear equations)
8 Problem Formulation Define decision variables (unit of scale) Define the linear relation between variables (write the linear equations)
Example 2 a dietitian is to combine a total of 5 servings of cream of mushroom soup, tuna, and green beans, among other ingredients, in making a casserole
9 Example 2 A dietitian is to combine a total of 5 servings of cream of mushroom soup, tuna, and green beans, among other ingredients, in making a casserole
Ingredient nutritions Each serving of soup has 15 calories and 1 gram of protein each serving of tuna has 160 calories and 12 gram of protein and each serving of green beans has 20 calories and 1 gram of protein
10 Ingredient Nutritions Each serving of soup has 15 calories and 1 gram of protein, each serving of tuna has 160 calories and 12 gram of protein, and each serving of green beans has 20 calories and 1 gram of protein