$1)$ A sales budget is given below for one of the products manufactured by the Key Co$.$:

January $21,000$ units

February $36,000$ units

March $61,000$ units

April $41,000$ units

May $31,000$ units

June $25,000$ units

The inventory of finished goods at the end of each month should equal $20\%$ of the next month's sales. However, on December $31,$ the finished goods inventory totalled only $4,000$ units.

Each unit of product requires three specialized electrical switches. Since the production of these specialized switches by Key's suppliers is sometimes irregular, the company has a policy of maintaining an ending inventory at the end of each month equal to $30\%$ of the next month's production needs. This requirement had been met on January $1$ of the current year.

Required:

Prepare a budget showing the quantity of switches to be purchased each month for January, February, and March, and in total for the quarter.