Pearl Products Limited of Shenzhen, China, manufactures and distributes toys throughout South East Asia. Three cubic centimeters $($cc$)$ of solvent H$300$ are required to manufacture each unit of Supermix, one of the company$$s products. The company is planning its raw materials needs for the third quarter, the quarter in which peak sales of Supermix occur. To keep production and sales moving smoothly, the company has the following inventory requirements:

The finished goods inventory on hand at the end of each month must equal $3,000$ units of Supermix plus $25\%$ of the next month$$s sales. The finished goods inventory on June $30$ is budgeted to be $16,250$ units.

The raw materials inventory on hand at the end of each month must equal one$-$half of the following month$$s production needs for raw materials. The raw materials inventory on June $30$ is budgeted to be $81,375$ cc of solvent H$300.$

The company maintains no work in process inventories.

A monthly sales budget for Supermix for the third and fourth quarters of the year follows.

Budgeted Unit Sales

July $53,000$

August $58,000$

September $68,000$

October $48,000$

November $38,000$

December $28,000$

Required:

$1.$ Prepare a production budget for Supermix for the months July, August, September, and October.

$3.$ Prepare a direct materials budget showing the quantity of solvent H$300$ to be purchased for July, August, and September, and for the quarter in total.