Tutorial, linear programming

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However when the factory manager sees the figures he points out that over the three month period there will not only be a restriction on blending hours, but in addition the heating and refining hours cannot exceed 1200 and 450 hours respectively during the three month period.

Required:

(a) Calculate the initial production plan for the period 1 June to 31 August as prepared by the management accountant, assuming blending hours are the only scarce factor. Indicate the budgeted profit or loss, and explain why the solution is the optimum.

(b) Calculate the optimum production plan for the period 1 June to 31 August, allowing for both the constraint on blending hours and the additional restrictions identified by the factory manager, and indicate the budgeted profit or loss.

(c) State the implications of your answer to (b) in terms of the decisions that will have to be made by XYZ Ltd. with respect to production during the period 1 June to 31 August after taking into account all relevant costs

(d) Under the restrictions identified by the management accountant and the factory manager, the shadow (or dual) price of one extra hour of blending time on the optimum production plan is £27.50. What is the shadow (or dual) price of one extra hour of refining time? Explain how such information might be used by management, and indicate the limitations inherent in the figures.

Question (3): BRONX

Bronxplc is in the process of preparing its budget for the coming year. The information from the marketing department indicates that sales demand is in excess of present plant capacity. Because equipment is specialized and made to order, a lead time in excess of one year is necessary on all plant additions.

Bronx produces three products and the estimated demand is as follows

X 90000 units

Y 34000 units

Z 46000 units

Production of these quantities is immediately recognized as being impossible. Practical capacity is 41000 machine hours in department 1 and 48000 machine hours in department 2.

Work-study estimates of machine time for each product are as follows:

X Y Z

Department 1 30 minutes 15 minutes 15 minutes

Department 2 15 minutes 7½ minutes 45 minutes

Standard costs and profits for the three products are as follows

X

Y

Z

£

£

£

Direct materials

6.00

4.00

17.25

Direct labour

2.00

1.00

3.50

Factory overheads

5.00

2.50

8.75

Selling & admin overheads

3.00

1.50

4.50

Profit (loss)

4.00

1.00

(4.00)

Selling price

20.00

10.00

30.00

Factory overhead is absorbed on the basis of direct labour cost at a rate of 250%; approximately 20% of the overheads are variable and vary with direct labour costs. Selling and administrative costs are allocated on the basis of sales value at the rate of 15%; approximately one half of this is variable and varies with sales value. The estimated overhead for the period is £525,000 for factory overhead and £250,000 for selling and administrative overhead.

The managing director has suggested that product Z should be eliminated from the product line and that the facilities be used to produce products X and Y. The sales manager objects to this solution because of the need to provide a full product line. In addition he maintains that the firm's regular customers provide, and will continue to provide, a solid base for the firm's activities and that these customers' needs must be met. He has provided a list of these customers and their estimated purchases are as follows:

Product X 40000 units

Product Y 16000 units

Product Z 8000 units

The managing director has reluctantly agreed to this proposal but has asked you, as the newly appointed accountant, to provide him with information of the maximum profit that can be obtained from the remaining capacity.

- Prepare an LP model that will calculate the optimum use of the uncommitted capacity left after the orders for the regular customers have been met. Use LINDO to find the solution to that model.

- What is the maximum profit for the period? Also calculate the profit that is lost as a result of imposing the minimum required supply for regular customers.

- Is there any other useful information available from the LINDO analysis of this system?