The feed, F, to three units (A, B and C) is split into three streams: FA, FB, and Fc. Two products are produced: P1 and P2 as shown in Figure Q1 below. FA A P₁ F FB B Fc P2 с Figure Q1 The yield in weight percent by unit is: Unit A (weight %) Unit B (weight %) Unit C (weight %) Product P1 P2 40 60 Each stream has values in £/kg as follows: Stream Value (£/kg) F 0.4 30 70 P1 0.6 50 50 P2 0.3 Because of capacity limitations, certain constraints exist in the stream flows: (ii) The total input feed must not exceed 10,000 kg/day. The feed to each of the units A, B and C must not exceed 5,000 kg/day. No more than 4,000 kg/day of P₁ can be used, and no more than 7,000 kg/day of P₂ can be used. In order to determine the values of FA, FB, and Fc that maximise the daily profit, prepare a mathematical statement of this problem as a linear programming problem. [20 marks]