2105623 course materials

LP and duality: questions explained

A supplemental review of dual variables and shadow-price ranges, based on the LP Exit Ticket. 23 slides with about 13 minutes of English narration.

Open the slides with narration

Press Play to begin. You can change the speed, read the transcript, or enable automatic continuation. Pause for the practice question on slide 21.

Study route

  1. Slides 2–10: deriving the dual and checking optimality
  2. Slides 11–20: shadow prices inside and outside the allowable interval
  3. Slides 21–23: practice, solution, and recap

Downloads

PowerPoint with embedded narration · Slide PDF · English transcript

Questions and follow-up

LP Exit Ticket and feedback. If you still have a question, include the slide number and the calculation or explanation that caused difficulty.

Original LP lesson · Class announcement

AI-generated narration using Microsoft Guy neural voice. Production quantities in this example are continuous. Updated November 2, 2026.