QUESTION $1[$LEARNING CURVE$](30$ marks$)$

Abdul Javed Ltd has trouble in the budgeting process because it finds it necessary

to quantify the learning effect as new products are introduced. Substantial product changes

occur and result in the need for retraining. An order for $40$ units of a new product has been

received. $19$ units have been completed. The first unit required $50$ hours of labour and a total

of $620$ hours of direct labour have been recorded for the $19$ units. The production manager

expects a $90\%$ learning effect for this type of work.

The following information is available per unit

Direct material R$60\mathrm{.}00$ per unit

Direct labour R$24\mathrm{.}00$ per direct labour hour.

Variable overhead R$1\mathrm{.}50$ per direct labour hour

Fixed overhead R$12000$ per four$-$week operating period.

There are $15$ direct employees working a five$-$day week, $8$ hours a day. Personal and other

downtime allowances account for $30\%$ of the total available time.

Required

a$.$ Determine whether the assumption of an $90\%$ learning effect is reasonable in this case. Use the

standard formula $y=b{x}^a$ where ; $(5)$

$y=$ the cumulative average direct labour hours per unit $($productivity$)$

$b=$ the average labour time per unit for the first batch

$x=$ cumulative number of batches produced

$a=$ index of learning

Round off $a=$ inde $x$ of learning to $3$ decimal places

b$.$ Calculate the number of direct labour hours likely to be required for an expected second order

of $30$ units. $(10)$

c$.$ Use the cost data above to estimate the product cost for the initial order, examining the problems

that may be created for budgeting by the presence of the learning effect. $(10)$

d$.$ Explain the conditions necessary for the learning curve to be realised. $(5)$