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Example of Model Construction (1 of 4)



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Example of Model Construction (1 of 4)

  • Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
  • A variable is a symbol used to represent an item that can take on any value.
  • Parameters are known, constant values that are often coefficients of variables in equations.
  • Data are pieces of information from the problem environment.
  • A model is a functional relationship that includes variables, parameters, and equations.
  • Example of Model Construction (2 of 4)
  • Variables: X = # units to produce (decision variable)
  • Z = total profit (in $)
  • Model: Z = $20X - $5X (objective function)
  • 4X = 100 lb of steel (resource constraint)
  • Parameters: $20, $5, 4 lbs, 100 lbs (known values)
  • Formal Specification of Model:
  • maximize Z = $20X - $5X
  • subject to 4X = 100
  • Example of Model Construction (3 of 4)
  • Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
  • Example of Model Construction (4 of 4)
  • Solve the constraint equation:
  • 4x = 100
  • (4x)/4 = (100)/4
  • x = 25 units
  • Substitute this value into the profit function:
  • Z = $20x - $5x
  • = (20)(25) – (5)(25)
  • = $375
  • (Produce 25 units, to yield a profit of $375)
  • Model Solution:
  • Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
  • Model Building:
  • Break-Even Analysis (1 of 9)
  • Used to determine the number of units of a product to sell or produce that will equate total revenue with total cost.
  • The volume at which total revenue equals total cost is called the break-even point.
  • Profit at break-even point is zero.

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