Please answer all parts of this question please with workings and explanations :)

Question 3 SafetyBox Ltd produced three products, "P", "C", and "R". The management team of SafetyBox Ltd is provided with the following information. Product P R Units Units Units Weekly sales demand (units) 2.500 3,000 2,000 Selling price (/unit) Material costs (/unit) Direct labour costs (/unit) 13 4 4 10 2 2 15 9 4 Total weekly conversion costs, including direct labour costs, are 41,000. Product P R Minutes Minutes Minutes Labour time (minutes/unit) 20 10 20 Machine time (minutes/unit) 6 5 8 The factory supervisor has identified "machine time" as the bottleneck. The maximum capacity of weekly machine production time is 550 hours. (Round up to two decimals in your calculation if required) Required: a) Calculate the throughput per machine minute for products "P", "C", and "R". You are required to show all workings. (7 marks) b) Assuming that the machine time bottleneck is fully utilised, calculate the quantities of each product that should be produced and sold to maximise the company's profit, and calculate the weekly profit. You are required to show all workings. (15 marks)