Intermediate: Limiting/key factors and a decision whether it is profitable to expand output by overtime B Ltd manufactures a range of products which are sold to a limited number of wholesale outlets. Four of these products are manufactured in a particular department on common equipment. No other facil¬ ities are available for the manufacture of these products.

Owing to greater than expected increases in demand, normal single shift working is rapidly becoming insufficient to meet sales requirements. Overtime and, in the longer term, expansion of facilities are being considered.

Selling prices and product costs, based on single shift working utilizing practical capacity to the full, are as follows:

Fixed manufacturing overheads are absorbed on the basis of machine hours which, at practical capacity, are 2250 per period. Total fixed manufacturing overhead per period is £427 500. Fixed selling and administration overhead, which totals £190000 per period, is shared amongst products at a rate of 10% of sales.
The sales forecast for the following period (in thousands of units) is:

Overtime could be worked to make up any produc¬ tion shortfall in normal time. Direct labour would be paid at a premium of 50% above basic rate. Other variable costs would be expected to remain unchanged per unit of output. Fixed costs would increase by £24570 per period.
Required:

(a) If overtime is not worked in the following period, recommend the quantity of each product that should be manufactured in order to maximize profit. (12 marks)

(b) Calculate the expected profit in the following period if overtime is worked as necessary to meet sales requirements.

(c) Consider the factors which should influence the decision whether or not to work overtime in such a situation.

Product (/unit) W X Y Z Selling price Product costs: 3.650 3.900 2.250 2.950 Direct materials 0.805 0.996 0.450 0.647 Direct labour 0.604 0.651 0.405 0.509 0.240 0.247 0.201 0.217 Variable manu- facturing o'hd Fixed manufacturing 0.855 0.950 0.475 0.760 o'hd Variable selling and 0.216 0.216 0.216 0.216 admin o'hd Fixed selling and 0.365 0.390 0.225 0.295 admin o'hd