Question $3(10$ marks; $18$ minutes$)$

Mellow $($Pty$)$ Ltd is a recently established medium sized organisation specialising in the cutting

and processing of marble tiles from raw marble blocks. Its current operating capacity is limited

to $120000$ machine hours per annum. Its sales mix consists of three products, for which the

budgeted selling price, direct wages and machine hours per square metre of output for the

forthcoming year are as follows:

Budgeted data per unit

The following data are also relevant:

a$.$ The sales manager is planning next year's sales and is of the opinion that the

following annual sales output estimates of each product are realistic and attainable at

the budgeted selling price per $m^2$ :

b$.$ The standard conversion ratio of raw marble to marble tiles, assuming no input losses,

is $10kg=1m^2.$ However, owing to the differing quality finishes of the respective

products, the standard materials input losses vary as follows:

Standard raw materials input losses:

c$.$ The cost of raw marble for the forthcoming year is estimated to be $R12$ per kg $.$

d$.$ Fixed production overheads are estimated to total R$500000$ for the year and are

absorbed on a machine hour basis. Variable production overheads are estimated to

be R$2,00$ per machine hour of output.

e$.$ Selling and administration costs are budgeted for the forthcoming year as follows:

Mellow $($Pty$)$ Ltd have engaged you as a consultant and have asked your advice in assisting

in their production and sales planning for the forthcoming year.

Required:

$3\mathrm{.}1$ Determine how many units $(m^2)$ of each product should be produced and sold next

year to maximise profit by making the best possible use of the scarce machine hours.