6. Three warehouses, \(\mathrm { P } , \mathrm { Q }\) and R , supply washing machines to four retailers, \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D . The table gives the cost, in pounds, of transporting a washing machine from each warehouse to each retailer. It also shows the number of washing machines held at each warehouse and the number of washing machines required by each retailer. The total cost of transportation is to be minimised. Formulate this transportation problem as a linear programming problem. You must define your decision variables and make the objective function and constraints clear.
You do not need to solve this problem.
(Total 7 marks)