A sales budget is given below for one of the products manufactured by the Key Company:

$\backslash$table$[[$January$,22,500$ units$],[$February$,37,500$ units$],[$March$,62,500$ units$],[$April$,42,500$ units$],[$May$,32,500$ units$],[$June$,26,500$ 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 totaled only $4,500$ 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:

a$.$ Prepare a budget showing the required production each month for January, February, March, and April.

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