Advanced: Formulation of initial tableau and interpretation of final tableau Bronx ltd 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 Ltd produces three products and the estimated demand is as follows:

Production of these quantities is immediately recognized as be1ng impossible. Practical capacity is 41 000 machine hours in department1 and 48000 machine hours in department2. Work study estimates of machine time for each product are as follows

Standard costs and profits for the three products are as follows:

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 at the rate of 15%;
approximately one half of this is variable and varies with sales value. The estimated overhead for the period is £525000 for factory overhead and £250000 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:

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 You decide to use mathematical programming to determine the optimal results from the uncommitted capacity and the final tableau of the linear programming model is as follows:

Required:

(a) Prepare the first tableau of the linear programming model to which the solution is given. (8 marks)

(b) What is the maximum profit for the period? Also explain how you would obtain information of how much profit is lost as a result of the imposition of the minimum sales constraints and indicate why this Information would be useful for product mix decisions. (7 marks)

(c) The managing director has requested an explanation of the meaning of the final tableau. You are required to provide an explanation of the meaning of each of the terms in the final tableau and provide any other information which would be of use that can be derived from the final tableau

Transcribed Image Text:

Product X 90 000 units Product Y 34 000 units Product Z 46 000 units