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

Warm Up Solve for x: 𝟖 𝟑𝒙−𝟓 +𝟏𝟓=𝟕𝟗

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

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

Homework Questions

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

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

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

Feasible Regions Plug each vertex into optimization equation (0,2) Point Equation 𝐳=−𝟎.𝟒𝒙+𝟑.𝟐𝒚 Total (0,2) 𝑧=−0.4 0 +3.2(2) (0,5) 𝑧=−0.4 0 +3.2(5) (1,6) 𝑧=−0.4 1 +3.2(6) (5,2) 𝑧=−0.4 5 +3.2(2) (5,0) 𝑧=−0.4 5 +3.2(0) (4,0) 𝑧=−0.4 4 +3.2(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)

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

Homework Textbook: 5-89 through 5-95a