Company making

Cycle Ltd is a company making stunt bicycles. It is a relatively new company and has so far tried to meet demand with little reference to the most profitable use of resources.
As the Management accounting trainee, you have come across a new technique that you have suggested the company use, linear programming. The management of Cycle Ltd have agreed to implement this and you have therefore collected all the information that you know about the costs, resource limitations and demands for both of the bicycles in production, The Kidd’ and The Pastrana’.
The Kidd currently makes a contribution of £1,200. It uses 12kgs of material, 10 hours of labour and 4 hours of machine time. The Pastrana makes a contribution of £1,500 uses 6kgs of material, 6 labour hours and 6 machine hours.
The maximum demand for The Kidd is 400 per month. You have a limit on the resources available per month with 9,000 kgs of material, 6,000 hours of labour and 4,200 machine hours. Required:
a) Formulate a linear programming problem (5 marks)
b) Determine the production levels required to maximise the monthly profit using the graphical approach, clearly showing the feasible region.
(12 marks)
The management of Cycle Ltd have ascertained that additional machines can be hired at £200 per hour and that additional materials can be purchased at an additional cost of £4 per kg.
c) Determine the shadow price of materials and machine hours and provide management with an assessment of whether it is worth purchasing additional hours of machine time and/or additional materials. Within this assessment explain the benefits and limitations of linear programming (13 marks) (Total 30 marks)

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