| | Film Series Four: Linear ProgrammingIn the first part of this programme we illustrate how two businesses can make decisions that help maximise profits as a result of using the mathematical technique of of linear programming. These video clips and animations can be viewed in isolation, or you can use our learning pathway and follow links to related material in our Question Bank.
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4.01 Introduction to Linear Programming
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).
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4.04 Linear Programming - Tomato Farmer (part one)
Now we return to Wight Salads with a different sort of problem, one that can be solved using linear equations. Hugh and his partners grow tomatoes exclusively. Although they grow many varieties, tomatoes are all that they produce for leading supermarket chains in the UK. Should they diversity into related products such as lettuce? Linear Programming helps them arrive at an answer. (Duration 12 minutes 36 seconds).
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4.06 Non-Linear Functions - Introduction
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).
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4.08 Introduction to Calculus
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).
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4.10 Calculus - Income Growth, Consumption and Savings
We saw in film two that we could estimate the effect on an economy of changes in income on consumption and on saving. We considered countries that have joined the EU in recent years that have typically lower incomes than the group they have joined. 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).
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4.11 Film Series Four - Conclusion
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 the next film it is of value in solving a whole range of economic problems. (Duration 1 minute and nine seconds).
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