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B2b. You have been asked to optimise a reactor temperature for an existing process. The amount of product being created in kg/ hour is given by the following empirical relationship with Temperature (T) : Flowrate of product (kg/hour)=ln(T), with T in C. The cost of delivering heating is related to the operating temperature (T) and any change in pumping from the nominal setting on the pump (P) and is represented by the following empirical relationship: Cost of heating (/ hour )=T(5P+1)2 The temperature cannot go above 40C, as above this temperature the solvent will degrade. i) If we sell the product for 20/kg, and there is no additional cost associated with further processing, what temperature and change from the nominal operating pump setting would be required to optimise the process and what is the profit? Show all steps used in obtaining your solution. [13 marks] ii) Comment on how the optimal temperature changes from the nominal pump setting. [3 marks] iii) What further process improvements could one make? [2 marks] iv) Comment on the mathematical properties of this optimisation problem, and what this says about the quality of your solution (max 50 words) [2 marks]