Peterkin Ltd makes three products, the 'Gadget', the 'Midget' and the 'Widget'. Each of the

products requires the use of labour and of materials, including a special material, 'Material

X$\text{'}.$ Manufacturing labour is equally capable of working on all three products.

Demand for all three products has increased strongly over recent months and is expected to

remain high.

Information about the products, relating to the foresecable future, is as follows:

Material X costs the business $0\mathrm{.}10$ a metre and the manufacturing workers are paid $8$ an

hour. The manufacturing workers are all employed on contracts that guarantee all $12$ of

them a $40-$hour week $($that is$,$ the manufacturing workers are paid $320$ a week, irrespective

of the amount of work carried out$).$ There are no other employment costs associated with

the workers. It is not possible to expand the staff by employing other manufacturing

workers and the existing ones are reluctant to work overtime.

Material X is in short supply and only $30,000$ metres a week are expected to be

available for the foreseeable future. The business holds no inventories of Material

$x.$ Supplies of it are received at the beginning of each week.

The business incurs manufacturing overheads that are believed to be partially fixed and

partially variable with manufacturing labour time. During two recent consecutive weeks,

these costs totalled $2,700$ in week one and $3,010$ in week two.

Output for those two weeks was as follows:

There have not been, nor are there expected to be in the foreseeable future, any

price changes, either of sales prices or of cost elements.

Required

$($a$)$ Prepare calculations that indicate whether it is the current level of staffing or the supply of

Material X that will constrain the business from meeting the expected demand for baskets.

$(6$ marks$)$

$($b$)$ Determine, with clear workings and justification $($including assumptions made$),$ the optimal

quantity of each product that the business should produce each week.

$[$c$]$ Descriac:

$($i$)$ the maximum amount that the business should be prepared to pay as an overtime rate to

the manufacturing workers, should any of them be prepared to work extra hours; and

$($ii$)$ the maximum amount that the business should be prepared to pay for any

additional quantities of Material X$.$

In each case explain how any additional resources would be deployed, if at all.

$($d$)$ Explain what steps the business might take to improve its profitability in the near future. $(2$