MotionSip manufactures drinking bottles and does wholesale to gyms throughout Sydney. Summarised results for the past two $(2)$ months reveal the following:

$\backslash$table$[[,$May,June$],[$Sales $($units of bottle$),9,600,10,600],[,$$$,$$$],[$Sales$,172,800,190,800],[$Materials$,49,000,52,500],[$Labour$,43,000,45,000],[$Overheads$,39,000,42,000],[$Total costs,$131,000,139,500],[$Operating profit,$41,800,51,300]]$

Required:

$($a$.)$ Calculate the fixed costs, the contribution margin and break$-$even points $(12$ marks$)$

$($b$.)$ In June, MotionSip is introducing a new product, with the blender function. The new bottle will sell for $$6$ more expensive than the normal bottle. The additional variable costs will be added based on the costs of a normal bottle: $$2$ for material, $$1\mathrm{.}5$ for labour and $$1$ for overhead. Fixed costs will increase by $$1,800$ per month due to both administrative and production changes. The company expects to reach a sale of $7,900$ bottles for this new product. According to the actual sale, what is the new break$-$even point for the company and the breakdown per product type? $(13$ marks$)$