The financial manager of Colatonic Ltd read about the plight of the local child welfare organisation which aimed to supplement its funds by making and selling cooking bags which can slow$-$cook meals or keep food warm for long periods. The financial manager approached the board of directors who agreed that the company should assist the organisation. After discussions with the president and treasurer of the welfare organisation the following budgeted information for $2024$ was gathered to assist with trying to improve the profitability and break$-$even quantity for the year: The fixed and variable manufacturing costs are estimated to be R$240000$ per annum and R$42$ per unit respectively. The selling price of the cooking bags will be R$120$ each. The selling and distribution costs are expected to total R$15000$ per month plus $5\%$ of sales. The administration costs are estimated at R$31000$ per month plus R$6$ per unit sold. $15000$ cooking bags are expected to be sold.

REQUIRED

Study the information provided by the child welfare organisation and answer the following questions

independently. The expanded contribution margin model must be used to answer questions $3\mathrm{.}1,3\mathrm{.}2$ and

$3\mathrm{.}4.$

$3\mathrm{.}1$ Calculate the break$-$even quantity. $(5$ marks$)$

$3\mathrm{.}2$ Calculate the sales volume required to achieve an operating profit of R$2112000.(5$ marks$)$

$3\mathrm{.}3$ Calculate the selling price per unit $($expressed to the nearest cent$)$ that will enable to

welfare organisation to achieve an operating profit of R$50$ per unit. $(5$ marks$)$

$3\mathrm{.}4$ Suppose the selling price is decreased by R$20$ per unit with the expectation that this

would increase the sales volume by $20\%.$ Is this a good idea? Motivate your answer with

the relevant calculations. $(5$ marks$)$

$3\mathrm{.}5$ Calculate the margin of safety $($in units$)$ if the selling price drops to R$110$ per unit with the

expectation that the fixed costs can be reduced to R$711900.(5$ marks$)$