Question 2: a) A firm has three categories of employees: juniors, seniors and supervisors. They earn $12, $18 and $24 per hour respectively. They have an output of 10, 16 and 22 units of product per hour respectively. The 250 employees of the plant have a total wage bill of $4,248 per hour and an hourly output of 3748 units. i) Place this into matrix form (Ax = b) to find the number of each worker employed by the firm. ii) Solve using the adjoint method for the number of each type of worker employed by the firm. (6 marks) b) A firm uses three machines to process its works Machine A is the most heavily used machine, machine B is used twice as often as machine C and half as often as machine A. If machine A produces a faultless product on 80% of occasions, machine B produces a faultless product on 70% of occasions and machine C loses 10% of its products to early faults, and of the product that remains, 90% is faultless. Find the probability that a faulty product has come from machine B. (4 marks)