The marketing department provided the following sales forecast:

July $ $50,000$

August $100,000$

September $500,000$

October $650,000$

November $550,000$

December $400,000$

January $200,000$

Ten percent of sales are for cash, $40\%$ of sales are collected after $30$ days, and the

remaining $50\%$ after $60$ days. Purchases, which are $80\%$ of sales, are incurred in the

month in which the sales are made. These goods are paid $30\%$ in cash and $70\%$ within

$30$ days. Distribution and administrative expenses are $$10,000$ per month, plus $1\%$ of

monthly sales. Start$-$up costs in July are $$30,000.$ Income taxes for the entire operating

period are paid in April and are $40\%$ of the profit. The monthly depreciation is

$$10,000.$ The company feels that it is necessary to maintain a minimum cash balance

of $$25,000$ during the selling season.

The cash balance on July $1$ is $$75,000.$