Kamariah receives an invoice for the purchase of $40$ batteries for RM$8,440$ on $31$ March $2023.$ Trade discounts are $5\%$ and $3\%$ and the cash discount terms are $8/10,5/30,$ n$/60.$ She pays the invoice on $19$ April $2023.$ She plans to sell the batteries by allowing $10\%$ of the cost for operating expenses and $28\%$ of the selling price for gross profit.

$($a$)$ Find the payment on $19$ April $2023.(4$ marks$)$

$($b$)$ Find the selling price and the net profit for each battery. $(4$ marks$)$

$($c$)$ After two months, Kamariah manages to sell $30$ batteries. The remaining $10$ batteries are sold by allowing $10\%$ markdown. Calculate the total sales made by Kamariah if all the batteries are sold.