1. Factor as many polynomials as you can.
Warm Up
Factor as many polynomials as you can.

2. 3-4 Linear Programming
A method for solving decision-making problems in which a linear expression is to be maximized or minimized

3. Background on Linear Programming
Developed by Leonid Kantorovich around the time of WWII
Further developed over following decades
Today, easily the most commonly used field for optimization
Economics, business management, transportation, technology, planning, production, etc

4. Linear Programming Steps
Define two variables, x & y.
Write a system of linear inequalities in x and y to represent the facts given in the problem.
Graph the system of inequalities to determine a feasible region.
Find the coordinates of each corner point of the feasible region.
Write a function in the form ax + by to be maximized or minimized.
Evaluate the function ax + by at each corner point.
Select the required minimum or maximum value, which will occur at one of the corner points, and note the values of x and y at that point.

5. flat and curved screen TVs

6. 3.4 Linear Programming Machine Flat Curved Hours Available A 1 h 2 h
flat and curved screen TVs
flat screen TV
or a curved screen TV.
Machine
Flat
Curved
Hours
Available A
1 h
2 h 16 B 9 C
4 h 24

7. The # of TV’s cannot be negative.
Machine
Flat
Curved
Hours
available
flat screen TVs x y
curved screen TVs A
1 h
2 h 16 B 9 C
4 h 24
The # of TV’s cannot be negative.

9. flat screen TV curved screen TV Test each corner:
(0,8) 𝑃= =320
(2,7) 𝑃= =400
(5,4) 𝑃= =460
(6,0) 𝑃= =360

12. Vitamin A 2 mg 1 mg 4 mg Vitamin B 3 mg 11 mg Vitamin C 25 mg 50 mg
Brand X
Brand Y
Minimum Daily Need
Vitamin A
2 mg
1 mg
4 mg
Vitamin B
3 mg
11 mg
Vitamin C
25 mg
50 mg
100 mg
Cost/Pill
6 cents
8 cents

13. Brand X
Brand Y
Minimum
Daily Need
Vitamin A
2 mg
1 mg
4 mg
Vitamin B
3 mg
11 mg
Vitamin C
25 mg
50 mg
100 mg
Cost/Pill
6 cents
8 cents

14. Corner Points (0,4) (1,2) (3,0.5) (4,0) 6(0)+8(4)=32 cents

15. Homework Section 3.4 Worksheet
6. Let x and y be positive integers such that 𝑥+𝑦≤13 and 3𝑥+𝑦≤24. Find the maximum value of: a. 𝑥+𝑦 b. 4𝑥+𝑦 c. 2𝑥+𝑦