Film Series Four: Linear Programming
In 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.
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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. (10 minutes 55 seconds)
View or comment on YouTube Permalink Download (103 MB) | Related MathsEG material Linear equations Inequalities / linear Feasible regions |
4.02 Linear Programming - Final Two Steps
In the previous section we established what is possible if our 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 programing. (9 minutes 14 seconds)
View or comment on YouTube Permalink Download (40 MB) | Related MathsEG material Optimisation (any method) |
4.03 Linear Programming - Conclusion
Summary of the value of linear programming in business decision making. (29 seconds)
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4.04 Linear Programming - Tomato Farmer (part one)
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. (12 minutes 36 seconds)
Erratum: About two minutes from the end, the audio narration swaps T and L in part of the explanation. The inequalities as they are written on screen are correct. We apologise for this mistake.
View or comment on YouTube: pt. 1 / pt. 2 Permalink Download (85 MB) | Related MathsEG material Feasible regions |
4.05 Linear Programming - Tomato Farmer (part two)
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. (4 minutes 4 seconds)
View or comment on YouTube Permalink Download (28 MB) | Related MathsEG material Optimisation (any method) |
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. (10 minutes 27 seconds)
View or comment on YouTube Permalink Download (89 MB) | Related MathsEG material General quadratic equation Nonlinear relations |
4.07 Non-Linear Functions - Labour Markets
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. (9 minutes 3 seconds)
View or comment on YouTube Permalink Download (75 MB) | Related MathsEG material General quadratic equation Nonlinear relations |
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. (6 minutes 20 seconds)
View or comment on YouTube Permalink Download (48 MB) | Related MathsEG material Differentiation of Polynomials Linear relations |
4.09 Calculus - Determining Marginal Revenue
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. (5 minutes 37 seconds)
View or comment on YouTube Permalink Download (26 MB) | Related MathsEG material Profit, average and marginal functions |
4.10 Calculus - Income Growth, Consumption and Savings
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. (5 minutes and 44 seconds)
View or comment on YouTube Permalink Download (40 MB) | Related MathsEG material Macro/ comparative statics |
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 this film it is of value in solving a whole range of economic problems. (1 minute and 9 seconds)
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