At March $31$ Streuling Enterprises, a merchandising firm, had an inventory of $39,000$ units, and it had accounts receivable totaling $$86,000.$ Sales, in units, have been budgeted as follows for the next four months:

$\backslash$table$[[$April$,60,800],[$May$,76,000],[$June$,91,200],[$July$,82,400]]$

Streuling's board of directors has established a policy to commence in April that the inventory at the end of each month should contain $40\%$ of the units required for the following month's budgeted sales. The selling price is $$4\mathrm{.}0$ per unit. One$-$third of sales are paid for by customers in the month of the sale, the balance is collected in the following month.

Required:

a$.$ Prepare a merchandise purchases budget showing how many units should be purchased for each of the months April, May, and June.

b$.$ Prepare a schedule of expected cash collections for each of the months April, May, and June.