Download - 3.2 Linear Programming
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3.2 Linear Programming
3 CreditsAS 91574
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• I can find the maximum or minimum of an objective function using the moving line approach
LEARNING OBJECTIVES
Linear Programming
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Define the unknowns
x =
y =
x = number of hectares of barley
y = number of hectare of swedes
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Define the constraints
LandCostMan power
Land x + y ≤ 20Cost 30x + 20y ≤ 480manpower x + 2y ≤ 36
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Profit
P = P = 100x + 120y
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the problem can be summarised as
maximise the profit P = 100x + 120y
subject to x + y ≤ 20 30x + 20y ≤ 480 x + 2y ≤ 36 x ≥ 0 y ≥ 0
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profit P = 100x + 120y
the gradient of this line is draw lines parallel to this to find the maximum
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this should give you x = 4 and y = 16
maximum profit is 100 x 4 + 120 x 16 = 2320
the farmer should sow 4 acres of barley and 16 acres of swedes
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SUCCESS CRITERIA
• I can find the maximum or minimum of an objective function using the moving line approach
Delta 4.02 page 56