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

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

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.

3.4 Linear Programming Machine Console Portable Hours Available A 1 h 16 B 9 C 4 h 24

The # of TV’s cannot be negative. Machine Console Portable Hours available x y A 1 h 2 h 16 B 9 C 4 h 24 The # of TV’s cannot be negative.

Constraints

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

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

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

Homework Page 112 #1-9 odds