The company wishes to maximise contribution. Set out the objective function and the constraints. Determine the optimum production of each product over the final quarter using the graphical approach to linear programming and calculate the optimum net profit for the final quarter of 2004. Calculate the shadow price of STX2 and explain how Jane may use it.
Emily Wye is currently working on the production schedules for next month. Her firm manufactures two types of ceramic grids:
|
| Type A £ | Type B £ |
| Selling price | 60 | 70 |
| Material X1 (at £2 per kg) | 3 | 6 |
| Material X2 (at £5 per kg) | 10 | 10 |
| Direct labour (grade 1) | 12 | 9 |
| Direct labour (grade 2) | 10 | 15 |
| Variable overhead | 5 | 7 |
Notes:
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Labour rates and maximum labour hours available in the next month are:
| Grade | Hourly rate | Max. monthly hours |
| 1 | £6 | 640 |
| 2 | £5 | Unlimited |
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Both products involve machine work, type A requiring 1 hour and B half an hour. The machine is available for 400 hours per month.
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Next month the company will have available 900 kg of X1. The firm can buy as much X2 as it wishes.
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Fixed overheads in the coming month will amount to £1950.
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The company wishes to maximise contribution. Set out the objective func- tion and the constraints.
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Determine the optimum output of each product next month using the graph- ical approach to linear programming. Calculate the optimum profit for the month.
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Calculate the amount of spare capacity available next month.
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Discuss three limitations of linear programming.
Jane Lane is the management accountant of a small manufacturing company. Jane normally gets involved in the production scheduling of the firm. She is currently working on this for the last three months of 2004, making use of her management accounting and linear programming skills.
The company manufactures components for rock climbing, including two types of ice axe, the X1 and the X2. During the last quarter of 2004, each X1 will have a selling price of £67 and each X2 a selling price of £78.
The cost of each axe is made up as follows:
|
| X1 (£) | X2 (£) |
| Materials: STX2 at £12 per metre | 15 | 18 |
| Labour: at £4.50 per hour | 9 | 18 |
| Variable overhead: at £5 per mc/hr | 10 | 15 |
In addition, monthly fixed manufacturing overheads are budgeted to be £2000 per month and fixed non-manufacturing overheads are budgeted to be £5000 for the three- month period.
The company will have the following resources available to it for the last quarter of the year: 800 metres of STX2, 2000 hours of labour and 1800 machine hours. The firm wishes to supply its retailers with no less than 150 of each type of axe during the final quarter.
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The company wishes to maximise contribution. Set out the objective function and the constraints.
-
Determine the optimum production of each product over the final quarter using the graphical approach to linear programming and calculate the optimum net profit for the final quarter of 2004.
-
Calculate the shadow price of STX2 and explain how Jane may use it.
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