Lecture 3

Lecture 3 - 540:311 DETERMINISTIC MODELS IN OPERATIONS...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 3: Chapter 3.1 - 3.3 Class Meeting: Thu Jan 27 th 10:20-11:40am Recitation: Introduction to Linear Programming Prof. W. Art Chaovalitwongse
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MIT and James Orlin © 2003 Example: GTC Problem Want to determine the number of wrenches and pliers to produce given the available raw materials, machine hours and demand.
Background image of page 2
MIT and James Orlin © 2003 Formulating the GTC Problem P = number of pliers manufactured W = number of wrenches manufactured Maximize Profit = Steel: Molding: Assembly: Pliers Demand: Wrench Demand: P,W 0 Non-negativity: 1.5 W + P 15,000 W + P 12,000 0.4 W + 0.5 P 5,000 P 10,000 W 8,000 .4 W + .3 P
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MIT and James Orlin © 2003 Reformulation P = number of 1000s of pliers manufactured W = number of 1000s of wrenches manufactured Maximize Profit = P,W 0 1.5 W + P 15 W + P 12 0.4 W + 0.5 P 5 P 10 W 8 400 W + 300 P Steel: Molding: Assembly: Pliers Demand: Wrench Demand: Non-negativity:
Background image of page 4
Graphing the Feasible Region 2 W P 4 6 8 10 12 14 2 4 6 8 10 12 14 We will construct and shade the feasible region one or two constraints at a time.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Graphing the Feasible Region W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Graph the Constraint: 1.5 W + P 15
Background image of page 6
Graphing the Feasible Region W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Graph the Constraint: W + P 12
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Graphing the Feasible Region W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Graph the Constraint: 0.4 W + 0.5 P 5 What happened to the constraint : W + P 12?
Background image of page 8
Graphing the Feasible Region W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Graph the Constraints: W 8 P 10
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
How do we find an optimal solution? W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Maximize z = 400W + 300P It is the largest value of q such that 400W + 300P = q has a feasible solution
Background image of page 10
How do we find an optimal solution? W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Maximize z = 400W + 300P Is there a feasible solution with z = 400W + 300P = 1200 ? z=1200
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Maximize z = 400W + 300P Is there a feasible solution with z = 2400 ? Is there a feasible solution with z = 3600 ? z = 2400 z=3600 How do we find an optimal solution?
Background image of page 12
W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Can you see what the optimal solution will be? z = 2400 z = 3600 Maximize z = 400W + 300P How do we find an optimal solution?
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
W P 2 4 6 8 10 12 14 2 4 6 8 10 12 14 What characterizes the optimal solution?
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 35

Lecture 3 - 540:311 DETERMINISTIC MODELS IN OPERATIONS...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online