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 facilities 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 £190 000 per period, is shared amongst products at a rate of 10 per cent of sales. The sales forecast for the following period (in thousands of units) is:
Product W ........................... 190
Product X ........................... 125
Product Y ........................... 144
Product Z ........................... 142
Overtime could be worked to make up any production shortfall in normal time. Direct labour would be paid at a premium of 50 per cent above basic rate. Other variable costs would be expected to remain unchanged per unit of output. Fixed costs would increase by £24 570 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.
(b) Calculate the expected profit in the following period if overtime is worked as necessary to meet sale requirements.
(c) Consider the factors which should influence the decision whether or not to work overtime in such a situation.

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Product (E/unit) Selling price Product costs: 3.650 3.900 2.250 2.950 0.805 0.996 0450 0.647 0.604 0.651 0.405 0.509 Variable manufacturing overhead 0.240 0.247 0.201 0.217 0.855 0.950 0.475 0.760 Variable selling and admin overhead 0.216 0.216 0.216 0.216 Fixed selling and admin overhead 0.365 0.390 0.225 0.295 Direct materials Direct labour Fixed manufacturing overhead