A company has two factories, one at Liverpool and one at Brighton.[20] In addition it has four depots with storage facilities at Newcastle, Birmingham, London and Exeter. The company sells its product to six customers C1, C2, , C6. Customers can be supplied either from a depot or from the factory direct (see Figure 19.1). Figure 19.1: Newcastle CI Liverpool C2 Birmingham C3 London C4 Brighton C5 Exeter C6 Factorics Depots Customers

Table 19.1: Supplier[a] Liverpool Brighton Newcastle Birmingham London Exeter Supplied to factory factory depot depot depot depot Depots Newcastle 0.5 Birmingham 0.5 0.3 London 1.0 0.5 Exeter 0.2 0.2 Customers C1 1.0 2.0 1.0 C2 1.5 0.5 1.5 C3 1.5 0.5 0.5 2.0 0.2 C4 2.0 1.5 1.0 1.5 C5 0.5 0.5 0.5 C6 1.0 1.0 1.5 1.5

[a] A dash indicates the impossibility of certain suppliers for certain depots or customers. The distribution costs (which are borne by the company) are known; they are given in Table 19.1 (in per ton delivered). Certain customers have expressed preferences for being supplied from factories or depots which they are used to.

The preferred suppliers are C1 Liverpool (factory) C2 Newcastle (depot) C3 No preferences C4 No preferences C5 Birmingham (depot) C6 Exeter or London (depots) Each factory has a monthly capacity given below which cannot be exceeded: Liverpool 150,000 tons Brighton 200,000 tons

Each depot has a maximum monthly throughput given below which cannot be exceeded:

Newcastle 70,000 tons

Birmingham 50,000 tons

London 100,000 tons

Exeter 40,000 tons

Each customer has a monthly requirement given below which must be met:

C1 50,000 tons

C2 10,000 tons

C3 40,000 tons

C4 35,000 tons

C5 60,000 tons

C6 20,000 tons

**Formulate this problem as a LP in which the objective is to minimize the total cost?