4. A furniture manufacturer has three workshops, \(W _ { 1 } , W _ { 2 }\) and \(W _ { 3 }\). Orders for rolls of fabric are to be placed with three suppliers, \(S _ { 1 } , S _ { 2 }\) and \(S _ { 3 }\). The supply, demand and cost per roll in pounds, according to which supplier each workshop uses, are given in the table below.
| \(W _ { 1 }\) | \(W _ { 2 }\) | \(W _ { 3 }\) | Available |
| \(S _ { 1 }\) | 12 | 11 | 17 | 30 |
| \(S _ { 2 }\) | 7 | 5 | 10 | 25 |
| \(S _ { 3 }\) | 5 | 6 | 8 | 10 |
| Required | 20 | 15 | 30 | |
Starting with the north-west corner method of finding an initial solution, find an optimal transportation pattern which minimises the total cost. State the final solution and its total cost.
(11 marks)