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$1300000.$ Murumba$$s 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 information To 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 A : Reduce 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 B: Reduce 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 C: Reduce 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 director$$s estimates of projected sales volume for the first six months is $2500$ units. $(1\mathrm{.}5$ marks$)$