Theseus Ltd manufactures a long$-$range 'Phantom' drone and employs a form of activity$-$based costing. Manufacturing and selling costs include unit level, batch level, product level and facility level costs. The unit level variable cost is $$45$ per unit, the cost per batch is $$100,$ the batch size is $30$ units and the sale price per unit is $$100,$ while the product level and facility level costs are $$20000$ and $$24000,$ respectively, per period. Assuming that the number of batches must be a whole number, how many units must be sold to earn a profit of $$54000$ before tax?