? QUESTION $4(12$ ?marks$)$

Ruff$-$Ryders $($Pty$)$ ?Ltd $($RR$)$ ?manufactures three different types of bikes namely

Amax, Bmax and Cmax. RR$$s financial year is $31$ ?December $2024.$ ?

Recently, RR has been experiencing a high$-$turnover rate which had an impact on the

production of the bikes. There are $5000$ ?estimated available labour hours for the

second quarter of the $2024$ ?financial year. RR wants to determine the optimal

production to maximise profit. Below is the estimated financial information for the

second quarter of the $2024$ ?financial year:

Rand per unit: Amax Bmax Cmax

Selling price $384552$

Direct material $5810\mathrm{.}5$

Direct labour $45\mathrm{.}57$

Variable production costs $2\mathrm{.}53\mathrm{.}55$

Sales commission $1\mathrm{.}523$

Expected demand $($units$)400500850$

Labour hours required per unit $2\mathrm{.}534$

REQUIRED:

Calculate the optimal production mix and make a recommendation to management.

?$(12$ ?marks$)$

Round your answers to two decimal places where required and show all your workings

clearly