1. 11D Applications of linear programming

2. There are three types of applications that we look at in Further Maths – Manufacturing problems (Ex 11C) – Blending problems – Transportation problems

3. Manufacturing problems There are two items being made (decision variables x and y) There are constraints on the number of each item to be made due to time, money, or labour. There is a profit/cost objective function to be maximised/minimised.

4. Blending problems One item is being made with raw material from three suppliers. Raw materials are being blended into a single item of a given size, weight, or volume. The material contains components in varying amounts that, after blending, must meet some minimal (or maximal) standard. There should be at least two components whose blended amount is restricted. The objective function is based on the differing costs of the material from the three suppliers and is to be minimised.

5. Example: Ex 11D, Q.1 You do Ex 11D, Q.2, 3

6. Transportation problems There is a single item being transported from exactly two factories to two distributors. Each distributor has a given demand which is the controlling influence, while each factory has a given level of production. The constraints are based on all shipments being non-negative quantities. The objective function is the transport cost, which must be minimised.

7. Example, Ex 11D, Q.4 You do Ex 11D, Q. 5, 6, 7, 9