Linear Programming

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Linear Programming

• Wyndor Glass Co.
• 3 plants
• 2 new products
• Product 1 glass door with aluminum framing
• Product 2 4x6 foot wood frame window

 
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Wyndor Glass Problem cont.

• Objective
• Determine what the production rates should be
  for the two products in order to maximize their
  total profit, subject to the restrictions imposed
  by the limited production capacities at each
  plant.

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Wyndor Glass Problem cont.

• Optimal Solution
• Product 1 2 batches/week
• Product 2 6 batches/week
• Profit - 36,000

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Intro. To Linear Programming

• Definition Programming Problems
• Concerned with the use or allocation of scarce
  resources (labor, materials, machines, and
  capital), in the best possible manner so that
  costs are minimized or profit is maximized.

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Intro. To Linear Programming

• Definition Linear Programming Problems
• The decision variables are non-negative
• The objective function is linear
• The constraint set is a set of linear equations
• Other programming problems
• Integer
• Non-linear (quadratic)
• Goal
• Paramteric

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Why wide use of Linear Programming?

• Wide variety of problems can be represented by an
  LP.
• There exist efficient techniques for solving LPs.
• Ease of analysis of data variation (sensitivity
  analysis)

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Formulation of LP Model

• Identify the decision variables.
• Identify the problem constraints and express the
  constraints as a series of linear equations.
• Identify the objective functions as a linear
  equation, and state whether the objective is
  maximization or minimization.

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Formulation of Wyndor Glass Model

• Identify the decision variables.
• x1 Number of batches of product 1 produced per
  week.
• x2 Number of batches of product 2 produced per
  week.
• Identify the problem constraints and express the
  constraints as a series of linear equations.
• Identify the objective functions as a linear
  equation, and state whether the objective is
  maximization or minimization.

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Formulation of Wyndor Glass Model cont.