AUBAIN Ltd manufactures a range of baths which it distributes to the market exclusively

through a major hypermarkets. The products have been developed over many years of

trading and cover all the sectors of the market $-$ from the Basic model to the Gold model.

Fabrice Foolchand, the company's sales and marketing director, has been carrying out an

extensive market research exercise with the assistance of his team. The following demand,

selling price and cost structure have been forecast for the coming year:

However, Fabrice has real concerns that the company will be unable to reach the necessary

levels of manufacturing output to keep up with the forecast demand. In particular, there has

been a recent history of industrial relations problems which have cut the effective operating

capacity.

Mr Krishen, the Human Resource $($HR$)$ manager, is aware of this risk and has made provision

for the recruitment of some sub$-$contract labour to cover such problems.

The following information is also available:

The company employs $40$ highly skilled staff in bath manufacture with a maximum

annual capacity of $70000$ direct labour hours. During the last financial year, industrial

action resulted in the loss of $20\%$ of that capacity. In planning for the new financial

year, it is recognised that further industrial action remains a possibility.

The HR manager has negotiated a further $7000$ hours of capacity to be provided by

sub$-$contract labour over the coming year.

Variable manufacturing costs include both labour costs and variable manufacturing

overhead.

Variable manufacturing costs are incurred at a rate of Rs$50$ per direct labour hour.

Fixed overhead is shared across the products, according to the space occupied by the

work$-$in$-$progress for each product line.

Required:

$($a$)$ Identify and quantify the limiting factor on the company's ability to meet the

expected demand for the year ahead.

$[6$ marks$]$

$($b$)$ Devise the optimal production plan for the year ahead and compute the expected

level of profits arising from the implementation of this plan.