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Simplex algorithm worksheet and solver (Decision maths)

Simplex algorithm worksheet and solver (Decision maths)

The first resource guides your students through the whole process of using the Simplex algorithm to solve a linear programming problem. The first page explains how the initial tableau is formed, how the objective function must be written and how the inequalities that represent constraints must be written as equations with the introduction of slack variables. The first exercise (11 questions) gives them the opportunity to practise writing the initial tableau correctly for different problems. Grids are provided so students focus their time and energy on only the values in the tableau. The next section describes how an iteration of the algorithm is performed and links the iterations to the graphical solution, showing how each iteration moves to a different vertex of the feasible region. There is then another exercise with 10 questions for students to practise performing iterations and finding the optimal solution. Again, grids are provided so students focus their time and energy on only the steps of the algorithm and the values in the tableau. Fully worked solutions are provided to all the questions in the exercises. The second resource is a spreadsheet that automatically solves any simplex tableau in 2/3 variables with 2/3 constraints - a useful resource for doing/checking solutions to other questions from a textbook or examination paper.
langy74
Linear programming problems - graphical solution (Decision maths)

Linear programming problems - graphical solution (Decision maths)

These resources are designed to aid the teaching and learning of using a graphical method to solve linear programming problems. The first resource introduces the idea of representing inequalities on graphs and finding the point(s) that maximise a given objective function. There are also some examples that require integer solutions so the optimal point is not at a vertex of the feasible region. The second resource provides practice of solving problems with a provided graph - these are examination style questions and involve considering how changes to the objective function may change the optimal point(s). The third resource has 2 example questions in context where the students must use a description of a problem to formulate the objective function and the non-trivial constraints, and then go on to solve the problem graphically. Grids are provided for all graphs and solutions are included for all questions.
langy74
Route inspection - resource to teach and practise the algorithm (Decision maths)

Route inspection - resource to teach and practise the algorithm (Decision maths)

This printable worksheet makes it easy to introduce the route inspection algorithm and will help your students understand how to apply the algorithm. The first page reminds students about Eulerian and semi-Eulerian graphs, how these are the types of graphs we require to solve the route inspection problem, and then has an example where you can introduce the idea of adding/repeating arcs to create the type of graph you need. The next page summarises the steps of the general algorithm and then the set of example questions begins. There are 14 questions in total, all with diagrams, with some requiring a closed route and some that do not. Fully worked solutions for all examples are provided.
langy74
Prim's and Kruskal's algorithms (minimum spanning tree) for Decision 1 maths

Prim's and Kruskal's algorithms (minimum spanning tree) for Decision 1 maths

This printable worksheet is a good way to get your class to practise using Prim's and Kruskal's algorithms to find the minimum spanning tree for a network. The sheet saves you or your students having to copy down any network or tables and allows you to focus your time on using the algorithms. The worksheet includes using Prim's on a network and on a matrix. Solutions are provided.
langy74
Resources to teach, practise and revise sorting and packing algorithms (D1)

Resources to teach, practise and revise sorting and packing algorithms (D1)

These resources save a lot time as they have ready-made examples you can project onto a board and students can work on the printable worksheets which saves them copying down questions and makes lesson time more productive. The resources cover bubble sort, shuttle sort and the first-fit algorithm. There are also resources which explain how to measure and compare the efficiency and order of algorithms. All answers are included to the exercises and revision material. Note that these resources were created for the OCR D1 module (4736) but would be useful resources for anyone teaching the algorithms mentioned.
langy74
Revision material for sorting and packing algorithms (Decision maths D1 - OCR 4736)

Revision material for sorting and packing algorithms (Decision maths D1 - OCR 4736)

These resources are a great way for your students to revise the key points they need to remember and understand about bubble sort, shuttle sort and the first-fit algorithms. The multiple choice questions are a quick way to check/revise the key knowledge, or this could be used as a quick assessment (answers provided) The sorting and packing practice worksheet has 2 pages of examination-style questions for students to attempt (worked answers included). The final resource is a 4-page document starting with all the required knowledge and skills listed on the first page, followed by 2 pages of examination-style questions (worked answers provided).
langy74
Resources on comparing the efficiency and order of algorithms (Decision maths D1 - OCR 4736)

Resources on comparing the efficiency and order of algorithms (Decision maths D1 - OCR 4736)

These resources can be used to introduce how the efficiency of algorithms can be compared and measured. In the first worksheet there is an example comparing bubble sort and shuttle sort, an example finding the order of an algorithm and then some examples using the order of an algorithm to estimate the time it will take to solve a problem of a particular size (fully-worked solutions are provided). In the second worksheet there are 12 exam-style questions on using the order of an algorithm to estimate the time it will take to solve a problem of a particular size. There is also the excel spreadsheet I created to generate examples - this can used to make as many more examples as you want.
langy74
Resources to teach and practise first-fit algorithm (Decision maths D1 - OCR 4736)

Resources to teach and practise first-fit algorithm (Decision maths D1 - OCR 4736)

After a few years of teaching packing algorithms by creating and working through examples on the board I got sick of it and created these resources. They make it easy to introduce, work through some examples and then there is another worksheet full of examples for students to attempt where the fully-worked solutions are already done, making it easy to check. The printable worksheets mean that students don't need to copy down lists of numbers or create tables to work on - this means they can spend the time just practising using the algorithm. There is also the excel spreadsheet I created to generate examples - this can used to make as many more examples as you want (instructions are on the spreadsheet).
langy74
Resources to teach and practise shuttle sort (Decision maths D1 - OCR 4736)

Resources to teach and practise shuttle sort (Decision maths D1 - OCR 4736)

After a few years of teaching sorting algorithms by creating and working through examples on the board I got sick of it and created these resources. They make it easy to introduce, work through some examples and then there is another worksheet full of examples for students to attempt where the fully-worked solutions are already done, making it easy to check. The printable worksheets mean that students don't need to copy down lists of numbers or create tables to work on - this means they can spend the time just practising using the algorithm. There is also the excel spreadsheet I created to generate examples - this can used to make as many more examples as you want (instructions are on the spreadsheet).
langy74