Leisure Ltd produces two types of bicycles, the leisure bicycle and the mountain bicycle. The leisure bike is a popular family bicycle, while the mountain bike is an all$-$terrain bicycle popular with sportspeople, Data relating to the two bicycles is as follows:

Selling price per unit Variable

$($R$)$

Leisure bicycle $1000$

manufacturing cost per unit $($R$)$

Mountain bicycle$2200$

$450$

$1210$

Required:

Sales representatives receive a commission of $5\%$ on the mountain bike and a $3\%$ commission on the leisure bike. Annual fixed costs total R$180000.$ The company has recently embarked on a marketing campaign of 'carfree living', which has seen the sale of its leisure bikes increase dramatically, with $80\%$ of the company's sales coming from the leisure bicycle.

Calculate the contribution per unit for each bicycle.

Assuming a constant sales mix, calculate:

$($I$)$ The weighted average contribution per unit $($il$)$ The weighted average contribution margin ratio $($ill$)$ The breakeven point in rands

$($iv$)$ The number of leisure and mountain bikes that must be sold in order to generate an after$-$target profit of R$500000($assume a tax rate of $30\%).$