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Maximizing Profit: Linear Programming for Agriculture Optimization

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This learning module explores the principles of linear programming through a real-world case study in agriculture. Participants will learn to optimize crop yields by utilizing the moving line approach to find maximum or minimum values of an objective function. The module outlines the process for defining variables such as hectares of barley and swedes, constraints like land and cost, and the profit function. Students will apply these concepts to determine optimal planting strategies to maximize profits, specifically calculating that planting 4 acres of barley and 16 acres of swedes yields a maximum profit of $2,320.

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Maximizing Profit: Linear Programming for Agriculture Optimization

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  1. 3.2 Linear Programming 3 Credits AS 91574

  2. Linear Programming Learning objectives • I can find the maximum or minimum of an objective function using the moving line approach

  3. Define the unknowns x = y = x = number of hectares of barley y = number of hectare of swedes

  4. Define the constraints Land Cost Man power Land x + y ≤ 20 Cost 30x + 20y ≤ 480 manpower x + 2y ≤ 36

  5. Profit P = P = 100x + 120y

  6. 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

  7. profit P = 100x + 120y the gradient of this line is draw lines parallel to this to find the maximum

  8. 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

  9. Success Criteria • I can find the maximum or minimum of an objective function using the moving line approach Delta 4.02 page 56

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