Check the attachment and answer the Questions.

In the Kingdom of the Republic of Idion there are five coal mines which have the following outputs and production costs: Mine output (tonnes/day production cost (E/tonne) 120 26 150 29 On A W N - 80 34 160 26 140 28 Before the coal can be sold, it must be 'cleaned' and graded at one of three coal preparation plants. The capacities and operating costs of these three plants are as follows: Plant capacity (tones/day) operating cost (E/tonne) A 300 N B 200 3 200 3All coal is transported by rail at cost of E0.5 per tonne kilometer, and the distances (in kilometers) from each mine to the three preparation plants are: Preparation Mines (Distance) plant 1 2 3 4 5 A 22 44 26 52 24 B 18 16 24 42 48 44 32 16 16 22 Required a) Using a transportation model, determine how the output of each mine should be allocated to the three preparation plants. b) Following the installation of new equipment at coal mine number 3, the production cost is expected to fall to $30 per tonne. What effect, if any, will this have on the allocation of coal to the preparation plants? c) It is planned to increase the output of coal mine number 5 to 180 tonnes per day which can be achieved without any increase in production cost per tonne. How will this affect the allocation of coal to the preparation plants