Introduction to Linear Programming Dominik Scheder Products - - PowerPoint PPT Presentation

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Mar 21, 2024 237 likes •940 views

Introduction to Linear Programming Dominik Scheder Products Resources production production production production production 1 +4 1 +4 = 1 +4 = = 14 1 +4 = = 14 8 +4 = = 28 1 +4 = = 14 8

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Introduction to Linear Programming

Dominik Scheder

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Products

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Resources

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production

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production

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production

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production

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production

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1× +4×

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1× +4× =

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1× +4× = = 14×

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1× +4× = = 14× 8× +4× = = 28×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98× 7 is a feasible solution.

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

4 4 is an infeasible solution.

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By growing 7 units of rice and nothing else, the farmer makes 98 units of money.

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By growing 7 units of rice and nothing else, the farmer makes 98 units of money. Can you compute the optimum?

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Upper Bounds

An Economists Perspective

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

???

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???

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???

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???

for for

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???

for for

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???

for for

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???

for for

35 × 2 + 28 × 5 = 210

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???

for for

35 × 2 + 28 × 5 = 210

A Good Deal?

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for for

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for for

1× +4× = = 14×

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for for

1× +4× = = 14× 1× +4× = 20×

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for for

1× +4× = = 14× 1× +4× = 20×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +4× = 20×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +4× = 20× 8× +4× = 36×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +4× = 20× 8× +4× = 36×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7× 1× +4× = 20× 8× +4× = 36×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7× 1× +4× = 20× 8× +4× = 36× 1× +2× = 12×

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for for

1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7× 1× +4× = 20× 8× +4× = 36× 1× +2× = 12×

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???

for for

35 × 2 + 28 × 5 = 210

A Good Deal?

The best you can get!

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1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98×

SLIDE 67 1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98×

SLIDE 68 1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98×

for for

35 × 2 + 28 × 5 = 210

SLIDE 69 1× +4× = = 14× 8× +4× = = 28× 1× +2× = = 7×

98×

for for

35 × 2 + 28 × 5 = 210

98× ≤ ≤ 210