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Murumba $($Pty$)$ Ltd $($Murumba$)$ manufactures and sells car brake pads. Murumba produced its $2024$ financial year budget based on the assumption that the entity would be able to sell the brake pads for R$6000$ each. The variable cost of each brake pad was projected at R$3000,$ and the annual fixed costs were budgeted at R$1300000.$ Murumbas fixed costs accrue evenly during the financial year.The entity requires a profit of R$3000000$ for the financial year in order to meet its target return on capital: R$1000000$ in the first six months and R$2000000$ in the remaining six months.The entity normally expects its sales to rise during the second quarter of the financial year. However, the June $2024$ management accounts show that sales volumes were not in line with expectations. During the first six months of the $2024$ financial year, variable costs were as projected, but at the budgeted selling price of R$6000,$ only $250$ units had been sold.Additional informationTo ensure that the entity still meets its required profit of R$2000000$ for the remaining six months, the following mutually exclusive alternative plans of action were developed:Plan AReduce the selling price by $10\%.$ The sales director believes that this will generate sales of $2700$ units during the remaining six months of the financial year. Total fixed costs and variable costs per unit will not be affected and will remain as budgeted.Plan BReduce variable costs per unit by $12,5\%$ through the use of less expensive raw materials. Fixed costs will not be affected. This will allow the selling price to be reduced by $7,5\%.$ Based on the reduced selling price and variable costs, the sales director believes that sales of $2200$ units will be achieved during the remaining six months of the financial year.Plan CReduce fixed costs by R$130000$ per annum. This will allow the selling price to be reduced by $5\%.$ Variable costs per unit will not be affected. Based on the reduced selling price, the sales director believes that sales of $2000$ units will be achieved during the remaining six months of the financial year.

Required:

$2\mathrm{.}1$ If no changes are made to the selling price or cost structure, determine the number of units that Murumba $($Pty$)$ Ltd had to sell during the first six months of the $2024$ financial year in order to:

$2\mathrm{.}1\mathrm{.}1$ Break$-$even. $(3$ marks$)$

$2\mathrm{.}1\mathrm{.}2$ Achieve a profit of R$1000000.(1\mathrm{.}5$ marks$)$

$2\mathrm{.}2$ Calculate the margin of safety ratio if no changes are to be made to the selling price or cost structure. Assume that the sales directors estimates of projected sales volume for the first six months is $2500$ units.

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