Quiz Two Answers

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Quiz Two Answers

• AGEC 352-R. Keeney
• September 27, 2006

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Most Limiting Resource

• It is the resource that defines the feasible
  space for a particular activity
• Answers the question What is the absolute
  maximum for Activity X?
• To find it
• Divide the RHS by the constraint coefficient
• Compare across the constraints
• Lowest one is most limiting

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Question 1 from Quiz 2

• Max Corn given Land
• 50/1 50 acres of corn
• Max Corn given Labor
• 350/8 43.75 acres of corn
• Max Corn given Capital
• 5000/42 119.04 acres of corn
• Since Labor is the lowest, it is the most
  limiting resource in corn production

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Question 2 from Quiz 2

• Max Oats given Land
• 50/1 50 acres of oats
• Max Oats given Labor
• 350/4 87.5 acres of oats
• Max Oats given Capital
• 5000/22 227.27 acres of oats
• Since Land is the smallest it is the most
  limiting resource for Oats

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Checking Feasibility (Q3 from Quiz 2)

• Given a C, S, A triplet, plug them into the
  constraints and see if the weak inequalities are
  satisfied
• C, S, A 0,0,0
• Feasible
• C, S, A 25,25,0
• Feasible
• C, S, A 40,0,10
• Not Feasible
• C, S, A 0,40,10
• Feasible

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Question 4 from Quiz 3

• Given an allocation plug in the values to
  constraints and objectives
• GM check
• 2375 so a) is true
• Land check
• Binding so b) is true
• Labor check
• Binding so c) is true
• Capital check
• Not Binding so c) is false

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Objective Penalty

• If forced to undertake one unit of an activity
  that is optimally set to zero, the objective
  penalty tells you how the objective variable
  would change
• Changes in the direction you dont want it to
  (negative for max positive for min)

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Question 5 from Quiz Two

• Objective Penalty for Oats production is -10
• Interpretation
• If we were forced to grow 1 acre of oats our GM
  would go down by 10 dollars
• Thus the statement is true

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Shadow Prices and Constraints

• Shadow price on land is 30.00 / acre
• We would be willing to rent up to 8.33 more acres
  as long as they cost no more than 30.00/acre
• 125/5 25 so a) is true
• We would be willing to lease out up to 6.25 acres
  as long as the rental fee is at least 30.00/acre
• 125/5 25 so b) is false

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Binding constraints

• RHS and LHS of land constraint are equal so it is
  binding
• A slack constraint is one where the RHS is not
  equal to the LHS
• Opposite of binding
• So c) is true and d) is false
• The answer is e) a c are true

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Allowable Increase (Activities)

• Allowable increase for activities refers to
  objective equation coefficients
• Answers the question how much could the GM per
  unit of corn go up and I would still produce 25
  acres of corn and 25 acres of beans
• Therefore question 7 is false

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Question 8

• The allowable increase for Soybeans is given as
  5.00
• The objective coefficient is 45.00
• An increase to 55.00 represents a change of 10.00
  which is bigger than the allowable increase
• Therefore, question 8 is false because we would
  expect the production plan to change if the
  soybean GM/acre went up by more than 5.00