Checkpoint
Complete the Checkpoint in your printout.
Optimization_2_ID
Explore
Watch topic videos, fill in guided notes and examples, and complete Checkpoints.
Optimization Video
Refer to your print out for this lesson section and video. Complete the guided notes section as you watch the video.
Examples
Refer to your print out or open your Student Worktext to each example. Follow along and complete the examples as you watch the videos.
Example 1
Given the graph, find the minimum and maximum values using the objective function, f(x, y) = 3x − y
Plan
Label the vertices.
Substitute vertices into objective function and evaluate.
Determine minimum and maximum values.
Implement
𝑓(0, 0) = 3(0) – (0)
𝑓(0, 0) = 0
𝑓(0, 5) = 3(0) – (5)
𝑓(0, 5) = −5 minimum
𝑓(6.5, 3.5) = 3(6.5) – (3.5)
𝑓(6.5, 3.5) = 16 maximum
𝑓(4, 1) = 3(4) – (1)
𝑓(4, 1) = 11
The vertices are named in a clockwise order in this curriculum when possible.
Explain
The vertex with the minimum value is (0, 5).
The vertex with a maximum value is (6.5, 3.5).
Example 2
Plan
Labeling the vertices with capital letters is not required. However, it may be helpful when determining all of the equations on a given coordinate plane.
Implement
Vertices: A (1, 1) B (0, 5)
C (2, 5) D (4, 4)
The vertices can also be written directly on the coordinate plane.
Lines:
ALTERNATE
(overline{CD}\m=-frac12\b=6\yleq-frac12x+6\overline{AD}\m=1\b=0\ygeq x)
Function: 𝑓(x, y) = y – x
𝑓(1, 1) = 1 – 1
𝑓(1, 1) = 0
Minimum
𝑓(0, 5) = 5 – 0
𝑓(0, 5) = 5
Maximum
𝑓(2, 5) = 5 – 2
𝑓(2, 5) = 3
𝑓(4, 4) = 4 – 4
𝑓(4, 4) = 0
Minimum
Explain
This problem has two minimums at (1, 1) and (4, 4), and a maximum at (0, 5).
Follow the directions to complete the Checkpoint, then check in with your instructor before continuing the lesson.
Quick test:
> and < signs (pasted into block editor)
43 = − log10(x) (entered with HTML from within block editor)
\[2\frac{1}{2}x\ +\ \sqrt{34y}\text{entered with mathQuill}\]
Long division Example
(As Custom HTML block)