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Introduction to Linear Programming

Description

This segment introduces the film series and examines how two businesses can make decisions that help maximise profits as a result of using the mathematical technique of linear programming. Belgian chocolates are famous the world over. But there are many different kinds of chocolate that can be made. How can the producer pick the best combinations within the various constraints imposed on the business? We see how the mathematics of linear programming can help to give an insight into this question. (Duration 10 minutes 55 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. Th

Subjects

metalproject | economics | mathematics | maths | linear programming | Social studies | L000

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Linear Programming - Final Two Steps

Description

If a chocolatier is to meet the constraints imposed on his business. How do we find the best combination that produces the maximum profit. We now follow the final two steps in linear programming. (Duration 9 minutes 14 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

metalproject | economics | maths | mathematics | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Programming - Conclusion

Description

Summary of the value of linear programming in business decision making. (Duration 29 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | maths | mathematics | linear programming | metalproject | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Programming - Tomato Farmer (part one)

Description

Hugh and his partners at Wight Salads grow tomatoes exclusively. Although they grow many varieties, tomatoes are all that they produce for leading supermarket chains in the UK. Should they diversify into related products such as lettuce? Linear Programming helps them to arrive at an answer. (Duration 12 minutes 36 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pat

Subjects

economics | maths | mathematics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Programming - Tomato Farmer (part two)

Description

Using linear programming we now take the last two steps to arrive at an answer about whether this tomato farmer should diversify into lettuce production. (Duration 4 minutes 4 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | maths | mathematics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Non-Linear Functions - Introduction

Description

The mathematics of Linear Programming is a useful tool. However, many relationships are not linear. How do we establish the price and quantity of a commodity if supply and demand functions are non-linear? Similarly, there may be non-linear relationships in the market for labour. And as we shall see, even where a demand curve is linear some of the important relationships that exist within such markets may not be linear. (Duration 10 minutes 27 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blo

Subjects

maths | mathematics | economics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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Non-Linear Functions - Labour Markets

Description

If a labour market has both non-linear supply and demand curves, how can we find the equilibrium wage rate and quantity of labour supplied? This segment looks at examples of non-linear supply and demand curves in several industries. (Duration 9 minutes 3 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

maths | mathematics | economics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Introduction to Calculus

Description

Now we extend the analysis of non-linear functions by beginning to illustrate the use of differential calculus. This is an essential tool for economists because in many areas of economics we are interested in the speed of change of functions as a means of dealing with economic problems. We will look at two simple examples here and develop further examples in our final film to extend our understanding of differential calculus. (Duration 6 minutes 20 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental buildi

Subjects

metalproject | economics | maths | mathematics | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Calculus - Determining Marginal Revenue

Description

This film examines the calculations for deriving marginal and total revenue with the linear demand curve of a firm with some monopoly power, and we calculate the effect on revenue of a change in output. (Duration 5 minutes 37 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | maths | mathematics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Calculus - Income Growth, Consumption and Savings

Description

Slovenia recently joined the EU and is experiencing sustained growth in income. If it succeeds in growing at an annual rate of 4 per cent for the next two years average income will be rather higher. But how will that growth in income affect consumption and saving? We use Differential Calculus to find out. (Duration 5 minutes and 44 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or vi

Subjects

maths | mathematics | economics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Film Series Four - Conclusion

Description

The mathematics of calculus is a very powerful tool of such widespread application in economics that it is essential that we understand its basic elements. As we shall see in this film it is of value in solving a whole range of economic problems. (Duration 1 minute and nine seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that use a variety of industries as examples, to examine how businesses can maximise profits by using the mathematical technique of linear programming. This series also examines non-linear functions. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Ques

Subjects

maths | mathematics | economics | metalproject | linear programming | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Introduction to Differentiation - How large should a University be?

Description

Making rational decisions often means thinking about small changes, and many of them revolve around the idea of the margin - the marginal change. A useful way of analysing marginal changes is by differentiation. (Duration 7 minutes 21 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

differentiation | economics | maths | mathematics | metalproject | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Conclusion to film 5.01

Description

Concludes the clip for differentiation and optimal University size. (Duration 2 minutes 13 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | maths | mathematics | differentiation | metalproject | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Finding the optimal number of floors in hotel construction - part one

Description

Up to a certain point, the higher the building, the lower the cost per floor. However at a certain point fixed costs rise dramatically to take into account the cost of deeper foundations and a stronger construction. In this film we introduce calculus to optimise spend and determine the appropriate number of floors to build. (Duration 5 minutes 18 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Quest

Subjects

economics | maths | mathematics | metalproject | integration | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Finding the optimal number of floors in hotel construction - part two

Description

Up to a certain point, the higher the building, the lower the cost per floor. However at a certain point fixed costs rise dramatically to take into account the cost of deeper foundations and a stronger construction. In this film we introduce calculus to optimise spend and determine the appropriate number of floors to build. (Duration 5 minutes). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

metalproject | maths | mathematics | economics | integration | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Finding the optimal number of floors in hotel construction - Conclusion

Description

Up to a certain point, the higher the building, the lower the cost per floor. However at a certain point fixed costs rise dramatically to take into account the cost of deeper foundations and a stronger construction. In this film we introduce calculus to optimise spend and determine the appropriate number of floors to build. (Duration 1 minutes 18 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Quest

Subjects

economics | maths | mathematics | metalproject | integration | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Differentiation - Prices in monopolistic markets - part one

Description

In this section we look at supermarket pricing, using differentiation to show that equilibrium price in monopolistic markets in higher than in competitive markets. (Duration 7 minutes 50 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

differentiation | maths | mathematics | metalproject | economics | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Functions - Budget Lines

Description

These films look at the use of linear functions to examine the spending options for a university student (duration 11 minutes 30 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that examines spending options in a number of contexts, and uses linear equations to explore constraints in markets. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

linear functions | maths | mathematics | economics | metalproject | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Differentiation - Prices in monopolistic markets - part two

Description

This film examines the relationship between monopoly power and elasticity, and applies this principle in order to understand why supermarkets mark up some goods much more than they mark up others. (Duration 4 minutes 44 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

differentiation | economics | metalproject | maths | mathematics | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Consumption Functions - East and West Germany

Description

This film is about how average income between regions in Germany varies greatly. The effects of these differences on expenditure patterns are examined by linear consumption functions. (Duration 9 minutes and 5 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that examines spending options in a number of contexts, and uses linear equations to explore constraints in markets. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank

Subjects

metalproject | maths | mathematics | economics | linear consumption functions | income | expenditure patterns | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Differentiation - Prices in monopolistic markets - part three

Description

Supermarkets have a much higher mark up on impulse items such as sweets. In this set we rearrange our formula and work out the elasticity implied in the mark up on any good. (Duration 4 minutes 24 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

differentiation | metalproject | economics | maths | mathematics | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Differentiation - Prices in monopolistic markets - Conclusion

Description

Differentiation has enabled us to understand why prices in monopolistic markets tend to be higher than in competitive ones. But an understanding of demand elasticity is essential to understanding price determination, not only in the supermarket, but also in markets generally. (Duration 4 minutes 26 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | metalproject | maths | mathematics | differentiation | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Linear Savings Functions - East and West Germany

Description

This film looks at how savings patterns in East and West Germany are related to income using a linear savings function. (Duration 5 minutes and 12 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that examines spending options in a number of contexts, and uses linear equations to explore constraints in markets. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank

Subjects

linear savings function | economics | maths | mathematics | metalproject | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Partial Differentiation - Complements and Substitutes

Description

In this section we use partial differentiation to determine the change in demand of one product when the price of another is changed. (Duration 10 minutes 37 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

maths | mathematics | economics | metalproject | differentiation | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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Partial Differentiation - The Multiproduct Firm - part one

Description

In this section we use the technique of partial differentiation to examine the pricing decisions in diversified organisations. (Duration 2 minutes 37 seconds). Part of a series of films from the METAL (Mathematics for Economics: enhancing Teaching and Learning) project that show how partial differentiation and integration are used to gain constructive insights into economics as a discipline. They are fundamental building blocks for a course of mathematics for economics. These video clips and animations can be viewed in isolation, or via the learning pathway links to related materials in a Question Bank.

Subjects

economics | maths | mathematics | metalproject | partial differentiation | Social studies | L000

License

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/

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