Gardner Company expects sales for October of $$246,000.$ Experience suggests that $55\%$ of sales are for cash and $45\%$ are on credit. The company collects $50\%$ of its credit sales in the month of sale and $50\%$ in the month following sale. Budgeted Accounts Receivable on September $30$ is $$67,000.$ What is the amount of cash expected to be collected in October?

a$.$ $$123,000.$

b$.$ $$202,300.$

c$.$ $$190,650.$

d$.$ $$135,300.$

e$.$ $$257,650.$