Agricultural Economics

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AgEc 301 Agricultural Economics I
Slide Set 18 Chapter 9
Linear Programming some extra stuff
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Some additional LP topics

• We have covered the basics of constructing LP
  models. There are many additional tips/tricks
  that you will want to learn as you go along.
• We will cover a few of those today.

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Transfer Rows

• In many applications you may wish to separate
  costs from revenues for activities.
• Multiple revenue options
• Multiple use options
• Joint products

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Transfer Rows

• One way to accomplish this, and force the solver
  to choose among alternative solutions is to use
  transfer rows.
• Transfer rows are equality constraints that must
  be binding in the solution

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Transfer Rows

• For example, if you have the activity produce
  barley you may wish to include only the per acre
  cost of production for this activity in the
  objective function.
• Activities sell barley, feed barley, and sell
  straw would then be included as separate
  activities.

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Transfer Rows
By setting up the problem this way, the solution
will choose between selling or feeding, along
with selling straw, all from the produce barley
activity.
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Production Mix Constraints

• Often times you will encounter a problem that
  requires one activity to be undertaken in fixed
  proportion to another.
• These can be easily handled using a combination
  of constraints and activities.

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Production Mix Constraints

• Consider our bat company example. Say that Big
  Stick takes an order from Sammy Sosa to custom
  make his bats.
• He requires one batting practice model for
  every 6 game models.

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Production Mix Constraints

• This suggests two activities, one for his BP
  model and one for his G model.
• We need to force the profit maximizing solution
  to contain 6 G models for each BP model produced.

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Production Mix Constraints

• This can be entered into the constraints and
  activities as

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Production Mix Constraints

• Note that a total use column must be included
  in your spreadsheet, that in this case would
  multiply the coefficients in the constraint by
  the number produced.

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Putting These Together

• Let us now reconsider our Big Stick, Inc.
  example.

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Big Stick

• Big Stick has been successful in building its
  demand through the success of their clients.
  They are quadrupling their capacity, and wish to
  reformulate their model using some of the
  techniques discussed here.

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Big Stick

• They want to add the two Sammy Sosa models, and
  in addition, whish to add activities for selling
  their bats so that they can separate the cost
  from the revenue in the model.

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Big Stick

• Additional information
• It costs 8.00 to manufacture an AG or MG bat,
  they sell for 30 and 40 respectively.
• It costs 12 and 35 to manufacture the SS-G and
  SS-BP models, they sell for 55 and 90
  respectively.