The president of the retailer Prime Products has just approached the company's bank with a request for a $$85,000,90$ day loan. The purpose of the loan is to assist the company in acquiring inventories. Because the company has had some difficulty in paying off its loans in the past, the loan officer has asked for a cash budget to help determine whether the loan should be made. The following data are available for the months April through June, during which the loan will be used:

a$.$ On April $1,$ the start of the loan period, the cash balance will be $$13,600.$ Accounts receivable on April $1$ will total $$168,000,$ of which $$144,000$ will be collected during April and $$19,200$ will be collected during May. The remainder will be uncollectible.

b$.$ Past experience shows that $30\%$ of a month's sales are collected in the month of sale, $60\%$ in the month following sale and $8\%$ in the second month following sale. The other $2\%$ is bad debts that are never collected. Budgeted sales and expenses for the three$-$month period follow:

$\backslash$table$[[,$April,May,June$],[$Sales $($all on account$),$$$240,000,$$$620,000,$$$289,000$

Required:

$1.$ Calculate the expected cash collections for april may and june and for the three months in total.

$2.$ Prepare a cash budget, by month and in total, for the three$-$month period.