1. Warm Up Solve for x: 𝟖 𝟑𝒙−𝟓 +𝟏𝟓=𝟕𝟗 𝒍𝒐𝒈 𝟑 𝒙+𝟐 − 𝒍𝒐𝒈 𝟑 𝟒𝒙=𝟓 𝟑𝒙−𝟏 >𝟏𝟏
I can use linear programming to solve
real world problems
Warm Up
Solve for x:
𝟖 𝟑𝒙−𝟓 +𝟏𝟓=𝟕𝟗
𝒍𝒐𝒈 𝟑 𝒙+𝟐 − 𝒍𝒐𝒈 𝟑 𝟒𝒙=𝟓
𝟑𝒙−𝟏 >𝟏𝟏
Verify your solution(s) to number 3 is correct

2. Warm Up
Solve for x:
𝟖 𝟑𝒙−𝟓 +𝟏𝟓=𝟕𝟗

3. Warm Up
Solve for x:
𝒍𝒐𝒈 𝟑 𝒙+𝟐 − 𝒍𝒐𝒈 𝟑 𝟒𝒙=𝟓

4. Warm Up Solve for x: 𝟑𝒙−𝟏 >𝟏𝟏
Verify your solution(s) to number 3 is correct

5. Homework Questions

6. Optimization – Feasible Regions
Given the following constraints, maximize and minimize the value of z if z=−0.4𝑥+3.2𝑦
𝑥≥0
𝑦≥0
𝑥≤5
𝑥+𝑦≤7
𝑥+2𝑦≥4
𝑦≤𝑥+5

7. Feasible Regions Graph constraints Rewrite equations in 𝑦=𝑚𝑥+𝑏 form
𝑥≥0
𝑦≥0
𝑥≤5
𝑦≤−𝑥+7
𝑦≥− 1 2 𝑥+2
𝑦≤𝑥+5

8. Feasible Regions
Identify vertices
0,2
0,5
1,6
5,2
5,0
(4,0)

9. Feasible Regions Plug each vertex into optimization equation (0,2)
Point
Equation
𝐳=−𝟎.𝟒𝒙+𝟑.𝟐𝒚
Total
(0,2)
𝑧=− (2)
(0,5)
𝑧=− (5)
(1,6)
𝑧=− (6)
(5,2)
𝑧=− (2)
(5,0)
𝑧=− (0)
(4,0)
𝑧=− (0)
6.4
16.0
18.8
4.4
−2.0
−1.6
Maximum of 18.8 occurs at 1,6 and
minimum of -2.0 occurs at (5,0)

10. Sandy Dandy Dune Buggies
Work in table groups
Each person will turn in their own paper

11. Homework
Textbook:
5-89 through 5-95a