Difference between revisions of "Linear programming"
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We covered topics on page 21 to 29 of the notes by Marlin, however, I did not focus on the mathematical details; we only consider the geometric viewpoint in 4G3. | We covered topics on page 21 to 29 of the notes by Marlin, however, I did not focus on the mathematical details; we only consider the geometric viewpoint in 4G3. | ||
The R-code used to draw the plot in the class handout | |||
<syntaxhighlight lang="sas"> | |||
plot(c(0, 100), c(0, 70), type = "n", xlab = expression(x[1]), ylab = expression(x[2]), asp = 1) | |||
abline(a=150, b=-1.6, lw=7) | |||
abline(a=1000/12, b=-10/12, lw=5) | |||
abline(a=500/8, b=-0.5, lw=3) | |||
abline(v=0, h=0) | |||
title(expression("Objective: Maximize 10"~x[1]~"+ 15"~x[2])) | |||
text(20, 55, expression("Inspection: 4"~x[1]~"+ 8"~x[2]~"+ "~x[5]~" = 500"), srt=332.5) | |||
text(35, 57, expression("Solder: 10"~x[1]~"+ 12"~x[2]~"+ "~x[4]~" = 1000"), srt=319.5) | |||
text(65.5, 50, expression("Placement: 16"~x[1]~"+ 10"~x[2]~"+ "~x[3]~" = 1500"), srt=301) | |||
text(2, 30, expression("Non-negativity: "~x[1]>=~"0"), srt=90) | |||
text(45, 2, expression("Non-negativity: "~x[2]>=~"0"), srt=0) | |||
delta=2 | |||
text(0+delta, 0+delta, "[0]") | |||
text(0+delta, 62.5-2*delta, "[1]") | |||
text(62.5, 31.25-1.5*delta, "[2]") | |||
text(87-delta, 10.9-1.0*delta, "[3]") | |||
text(93.75-2.1*delta, 0+1.0*delta, "[4]") | |||
</syntaxhighlight> | |||
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| 19 January | | 19 January | ||
Revision as of 20:13, 20 January 2015
| Class date(s): | 07 January 2015 | ||||
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References
Dr. Marlin has made a great, short e-book on Linear Programming. You will find reading his notes very rewarding, and a great supplement to the class lectures.
Resources
Scroll down, if necessary, to see the resources.
| Date | Class number | Topic | Slides/handouts for class | Video file | References and Notes |
|---|---|---|---|---|---|
| 07 January | 01B |
|
Video | ||
| 12 January | 02A |
|
Video |
We covered topics on page 11, 13, 14 and 17 of the notes by Marlin (see comment above). | |
| 14 January | 02B |
|
Video |
We covered topics on page 21 to 29 of the notes by Marlin, however, I did not focus on the mathematical details; we only consider the geometric viewpoint in 4G3. The R-code used to draw the plot in the class handout plot(c(0, 100), c(0, 70), type = "n", xlab = expression(x[1]), ylab = expression(x[2]), asp = 1)
abline(a=150, b=-1.6, lw=7)
abline(a=1000/12, b=-10/12, lw=5)
abline(a=500/8, b=-0.5, lw=3)
abline(v=0, h=0)
title(expression("Objective: Maximize 10"~x[1]~"+ 15"~x[2]))
text(20, 55, expression("Inspection: 4"~x[1]~"+ 8"~x[2]~"+ "~x[5]~" = 500"), srt=332.5)
text(35, 57, expression("Solder: 10"~x[1]~"+ 12"~x[2]~"+ "~x[4]~" = 1000"), srt=319.5)
text(65.5, 50, expression("Placement: 16"~x[1]~"+ 10"~x[2]~"+ "~x[3]~" = 1500"), srt=301)
text(2, 30, expression("Non-negativity: "~x[1]>=~"0"), srt=90)
text(45, 2, expression("Non-negativity: "~x[2]>=~"0"), srt=0)
delta=2
text(0+delta, 0+delta, "[0]")
text(0+delta, 62.5-2*delta, "[1]")
text(62.5, 31.25-1.5*delta, "[2]")
text(87-delta, 10.9-1.0*delta, "[3]")
text(93.75-2.1*delta, 0+1.0*delta, "[4]")
| |
| 19 January | 03A |
|
Video |