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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)

Sample Solution

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April 7, 2018: the best meal of my life. Back to Hopedale, four years later, except this time, we upgraded our living arrangements to an old steam-powered river boat a mile or two down the road. Smiley, the caretaker of the river boat, fixed a low country boil after we arrived back from the familiar channels of my 6th grade trip. With enough crawfish, shrimp, andouille sausage, and corn on the cob to fill up two 120-quart igloo coolers, we ate until the heavenly, creole food grew cold (about 3 or so hours). Our mouths on fire from the pounds of crab boil and Cajun seasoning mixed into the boiling water, we sat on the top deck of the riverboat and watched on CBS as Patrick Reed, to our dismay, sweep the field at The Masters.

The muscular red drum broke the surface of the wind-rapped water, attem

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