1. Review Homework Page 190-193

2. Rocket City Math League There are five levels of three rounds of individual testing that range from Pre-Algebra to Calculus, and two levels of an Inter-School Test. Trophies are mailed to the top ranked students and schools at the end of the year. The interschool test is a group test. There are 15 questions and the entire group submits one answer sheet.

3. Rocket City Math League International Math Competition 2015-2016 testing dates are as follows Interschool: November 2nd - 15 th Senior*NOVEMBER 5 th 0 period ******* *Junior*NOVEMBER 12 th 0 period ******* Round 1: January 11th - 24th Round 2: February 8th - 21st Round 3: March 7th - 20th

7. 5) x=# of hours babysitting y=# of hours as a cashier x+y≤20 4000x+5000y≥80000

8. Linear Programming Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given situation. (Optimization 최적화 ) 선형계획법

9. Linear Programming You have started a school supply manufacturing company. You make two types of mechanical pencils, type A and type B. Using the information below, write 4 inequalities (1-4) and the objective quantity (function). (#5) 1.Your equipment can be programmed to make no more than 10 cases of pencils per hour. 2.Your company must produce at least 2 cases of type A 3.and at least 3 cases of type B. 4.The amount of type B must be less than or equal to 2 more than type A. 5.Your profits per hour are determined by the profit of $5 for each case of type A and $6 for each case of type B.

10. Bounded/Unbounded The feasible region is the solution set of the intersection of the constraints (inequalities). 실행가능한 영역 If the feasible region is bounded – is closed and makes a shape. There are both a minimum value and a maximum value.

11. Unbounded Feasible Region If the feasible region is unbounded – open on at least one side, there is only a minimum or maximum not both.

12. How to determine the Min and Max 1.Determine the coordinates of the vertices of the feasible region by graphing the inequalities. 2.Substitute the values into the function (objective quantity). [C=2x+y or f(x,y)=2x+y] 3.Compare the values to determine the highest and lowest values. The maximum value is the number calculated for the vertex.

13. Bounded Feasible Region Four vertices make up the bounded feasible region. (0,80) (20,60) (0,0) (50,0) If we are given the objective function, C=2x+3y, we would calculate C for each of the 4 points. C=2x+3y (0,80) 2(0) + 3(80) = 240 (20,60) 2(20)+3(60) = 220 (0,0) 2(0) + 3(0) = 0 (50,0) 2(50) + 3(0) = 100 The minimum value is 0 at (0,0) and the maximum value is 240 at (0,80)

14. Unbounded Feasible Region (3,2) (0,8) (9,0) Three vertices make up the unbounded feasible region. (0,8) (3,2) (9,0) If we are given the objective function, C=10x+8y, we would calculate C for each of the 3 points. C=10x+8y (0,8) 10(0) + 8(8) = 64 (3,2) 10(3) + 8(2) = 46 (9,0) 10(9) + 8(0) = 90 Since as we go closer to the open (unbounded) area, the numbers get larger, there is no maximum value. The minimum value is 46 at (3,2)

15. Linear Programming You have started a school supply manufacturing company. You make two types of mechanical pencils, type A and type B. Using the information below, write 4 inequalities (1-4) and the objective quantity (function). (5) 1.Your equipment can be programmed to make no more than 10 cases of pencils per hour. 2.Your company must produce at least 2 cases of type A 3.and at least 3 cases of type B. 4.The amount of type B must be less than or equal to 2 more than type A. 5.Your profits per hour are determined by the profit of $5 for each case of type A and $6 for each case of type B. Determine the inequalities and graph them

16. 1 4 2 3 B≥3 A ≥2 A+B≤10 B ≤A+2

17. Linear Programming A method for finding a maximum and minimum value of a function over a given system of inequalities with each inequality representing a constraint (limitation). The feasible region is the solution set of the intersection of the constraints (inequalities).

18. 1 4 2 3 B≥3 A ≥2 A+B≤10 B ≤A+2 f(2,3)=28 (min) f(2,4)=34 f(7,3)=53 f(4,6)=56 (max) Feasible region

19. Practice Page 197

22. Homework page 198-199