A manufacturer is trying to determine the combination of two products, A and B, that should be produced. Each product passes through a three-stage production process: Stages I, II and III. For product A Stage I takes three hours of labour, Stage II four hours and Stage III one hour. For product B the comparable data are four hours, two hours and two hours. Labour hours currently cost £4.50 per hour. Product A sells for £38 a unit and B for £40. At present 11 people are employed on Stage I, 12 on Stage II and 10 on Stage III, with all employees working 40 hours each week.

(a) Formulate this problem in terms of determining the profit-maximising combination of the two products on a weekly basis.

(b) Solve the problem graphically.

(c) Confirm the solution using simultaneous equations.

(d) Identify the binding and non-binding constraints.

(e) Undertake sensitivity analysis on each of the binding constraints and evaluate the management information that this generates.

(f) What rate of overtime should the firm be willing to pay its employees?