Lesson 4 Linear Programming Intro Warm Up P

Lesson 4, Linear Programming Intro

Warm Up • P. 63 “Think About This Situation” • 10 minutes!

Notes – Schedule (pop quiz one day in here) TODAY – Lesson 4, Investigations 1 -2 OTL – OYO p. 73, OYO p. 77 Sign up on deltamath. com, teacher code: M/T – POW #9 review, Lesson 4, Investigations 3 -4 • Next Th/F – review homework, MOREs in class and for OTL • M/T (11/19 -20)before thanksgiving • • – Test on Lesson 4

Individual Test Corrections • After school Tues or before school Wed (only options!) • Test correction seminar (45 min) • We will correct and go over the problems • Gain up to 5 points on your score (total is out of 25)

Notes: Unit 1, Lesson 4 Linear Programming • Definitions: • Feasible/Non-feasible Region – Feasible – where it is possible – Non-feasible – where it isn’t possible • Constraints – Limits – Minimums or maximum values – Defines what is possible

Feasible region, income/cost • Feasible region when income is greater than costs: (I > C) – Not shaded in • Constraints: – x and y have to be positive

Notes: Solving/Graphing Inequalities (POW #9) • Solving inequalities – Just like other equations, except for 1 exception • If you have divide by a negative number, you have to flip the sign • If it is ≤, and you divide by a negative #, it becomes only > (same is true of the reverse) • 3 x + 6 y ≤ 8 • 3 x – 6 y ≤ 8

Notes: Solving/Graphing Inequalities (POW #9) • From a graph: • 2≥x • Which is the feasible region? A or B? • A • How about x ≥ 2? • B A B

Lesson 4, Investigation 1 • #1 with a partner • #2 – “guess and check” strategy – – – Group 1 check all y=500 points Group 2 check all y=400 points Group 3 check all y=300 points Group 4 check all y=200 points Group 5 check all y=100 points Group 6 check all y=0 points • #3 –what is the region? , maximum profit?

• #3 A FEASIBLE REGION

Lesson 4, Investigation 2 (#1 -3) • We can do the same thing we did by guess and check by creating algebraic models • If assembly time for IT-95 is 0. 6 hrs and time for IT-2000 is 0. 3 hours and we can’t exceed 240 hours of time, what equation can represent that? • 0. 6 x + 0. 3 y ≤ 240