One of the products that the sporting$-$goods retail chain, Sports World, sells is parachutes. In the first quarter of $2024,$ Sports World sold $650$ parachutes. Budgeted sales for the remainder of $2024($in units$)$ are: $700$ in Quarter $2,800$ in Quarter $3,$ and $900$ in Quarter $4.$ Sports World's selling price is $$500$ per parachute. All Sports World's sales are credit sales. Sports World collects $80\%$ of its sales in the quarter in which it made the sale and the remaining $20\%$ in the following quarter. At the beginning of the second quarter, Sports World had $320$ parachutes in its merchandise inventory that it had purchased for $$375$ each. Sports World's policy is to have $40\%$ of next quarter's sales in merchandise inventory $($in units$)$ at the beginning of each quarter. Sports World purchases its merchandise on credit, and it pays for $100$ percent of its purchases in the quarter following the purchase.

Please prepare the following budgets for Sports World parachute product line for the third quarter of $2024.$

a$)$ Purchases of merchandise $($parachutes$)$ in dollars

b$)$ Cash collections $($receipts$)$ budget from sales of merchandise $($parachutes$)$ in dollars

c$)$ Cash payments $($disbursements$)$ budget for purchases of merchandise $($parachutes$)$ in dollars