Vaughan Ltd makes 2 different types of shoe, Brogue and Casual, each using the same leather and the...

Question

Vaughan Ltd makes 2 different types of shoe, Brogue and Casual, each using the same leather and the same skilled labour. The costs of the products per unit of production are as follows:

Brogue	Casual
£	£
Selling price	96	80
Materials @ £3 per Kg	24	12
Labour @ £12 per hour	36	36
Other variable costs	12	12
Allocation of fixed costs	12	12
Profit per unit	12	8

The company is drawing up production plans for the month of June 2012. The anticipated maximum demand in the period is for 50 pairs of Brogues and 80 pairs of Casuals.
There are only 640kg of material and 300 hours of labour available in the period.
The company wishes to maximise profit in the period
Required

Formulate a linear programming model for this problem. (5 marks)
Prepare the initial tableau if the problem is to be solved using simplex. (5 marks)
Use the graphical method to determine how many of each type of boot should be produced. (12 marks)
What are the shadow prices of materials and labour? (8 marks)
If extra labour became available at £18 per hour should they be employed? If so how many extra hours should be bought? (10 marks)
By how much would the contribution of Casual shoes have to increase by to change your decision in part (c)? (10 marks)

Bramble Ltd makes 2 different types of boots, Premier and Champion, each using the same leather and the same skilled labour. The costs of the products per unit of production are as follows:

Premier	Champion
£	£
Selling price	80	60
Materials @ £8 per Kg	4	3
Labour @ £15 per hour	15	10
Other variable costs	12	8
Allocation of fixed costs	30	20
Profit per unit	19	19

The company is drawing up production plans for the 3 months to 30 June 2011. The anticipated maximum demand in the period is for 800 pairs of each type of boot.
There are only 630kg of material and 1500 hours of labour available in the period.
The company wishes to maximise profit in the period
Required

Formulate a linear programming model for this problem. (8 marks)
Prepare the initial tableau if the problem is to be solved using simplex (5 marks)
Use the graphical method to determine how many of each type of boot should be produced (12 marks)
What are the shadow prices of materials and labour? What do these prices mean? (10 marks)
If new supplies of leather became available at £12 per kg should they be purchased? If so how much extra material should be bought? (8 marks)
By how much would the contribution of champion boots have to increase by to change your decision in part (c)? (7 marks)

Mr. Larsson is an accountant who prepares final accounts for his clients. Work arrives at his office randomly at a rate of 8 per month. The times taken to complete the work form an exponential distribution with a mean of 3 days. There are 25 working days in each month.

Mr. Larsson is considering employing an apprentice to do the basic calculations on each job before he does the complicated parts. This should enable the completion of mean of 2 days, though the distribution will still be exponential.

Describe the steps involved in taking a scientific approach to management problems. (10 Marks)

For the current situation and then with the employment of the apprentice calculate the following:

Values for ?, µ and ? (6 marks)
The queue length and waiting time for clients including and excluding the service time (12 marks)
The probability that there will be more than 2 customers waiting (6 marks)
The probability that a client will wait (including service) for more than 2 months to have his accounts completed (6 marks)

Do your calculations suggest that the apprentice should be employed? What other factors are relevant to making that decision? (10 marks)

Gardener Ltd are considering building a new factory in Leicester. Seven tasks must be performed build the new factory and estimates of the duration for each task are shown below along with the precedence relationships for these tasks.

TASK	Optimistic Estimate (days)	Most Likely Estimate (days)	Pessimistic estimate (days)	Immediate predecessors
A	4	8	10	-
B	1	3	4	-
C	3	7	10	A
D	1	7	13	A
E	1	3	5	B,D
F	7	8	10	E
G	6	7	10	C

Gardener Ltd will receive a subsidy of £500,000 if it is completed in the next 22 days.

Explain why project management is a useful tool for managers (7 marks)
Draw the network diagram for this project and identify the critical path (7 marks)
Find the estimate for mean and variance of the duration of each activity and the mean duration of the critical path (14 marks)
Calculate the probability of completing the project within 22 days, stating any assumptions that you make? (12 marks)
What action could be taken to improve the chances of completion within 22 days? (10 marks)

005_iisu5k-jnnpyrue.docx

Robert · Accepted Answer

1. Vaughan Ltd makes 2 different types of shoe, Brogue and Casual, each using the 
same leather and the same skilled labour. The costs of the products per unit of 
production are as follows: 
 Brogue Casual 
 £ £ 
Selling price 96 80 
Materials @ £3 per Kg 24 12 
Labour @ £12 per hour 36 36 
Other variable costs 12 12 
Allocation of fixed costs 12 12
Profit per unit 12 8
The company is drawing up production plans for the month of June 2012. The 
anticipated maximum demand in the period is for 50 pairs of Brogues and 80 pairs of 
Casuals. 
There are only 640kg of material and 300 hours of labour available in the period. 
The company wishes to maximise profit in the period
Required 
(a) Formulate a linear programming model for this problem. (5 marks) 
Answer: 
Maximize profit: 12*b+8*c (objective function) 
subject to  
constraint 1: 8*b+4*c 0 (non-negative constraint)
where b = no. of units of style brogue and 
c= no. of units of style casual
(b) Prepare the initial tableau if the problem is to be solved using simplex. (5 marks) 
Answer: 
Initial Tableau: 
8 4 1 0 0 0 640 
3 3 0 1 0 0 300 
1 0 0 0 1 0 50 
0 1 0 0 0 1 80 
-12 -8 0 0 0 0 0
(c) Use the graphical method to determine how many of each type of boot should be 
produced. (12 marks) 
Answer: 
 
 
The points of interest are: (0,80),(20,80),(50,50),(50,0) 
Profits for these points are as follows: 
(0,80): Profit = 12*0+8*80 = 640 
(20,80): Profit = 12*20+8*80 = 880 
(50,50): Profit = 12*50+8*50 = 600+400 = 1000 
(50,0): profit = 12*50+8*0 = 600
Thus, Profit is maximized when b=50 and c = 50 
(d) What are the shadow prices of materials and labour?  (8 marks) 
Answer: 
Shadow price of material: 1 
Shadow price of labour: 1.333 
(e) If extra labour became available at £18 per hour should they be employed? If so 
how many extra hours should be bought? (10 marks) 
Answer: No, Extra labour should not be employed at this price as the individual 
profits become negative. The analysis is shown below: 
 
 
(f) By how much would the contribution of Casual shoes have to increase by to change 
your decision in part (c)? (10 marks) 
Answer: 
The sensitivity analysis report is shown as follows: 
 
 
From the report, it is clear that the allowable increase for casual shoes is 4 units. 
Thus, on increasing the units of casual by 4, profits change. 
 
2. Bramble Ltd makes 2 different types of boots, Premier and Champion, each using the 
same leather and the same skilled labour. The costs of the products per unit of 
production are as follows:

Vaughan Ltd makes 2 different types of shoe, Brogue and Casual, each using the same leather and the same skilled labour. The costs of the products per unit of production are as follows: Brogue Casual...

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