Tonga Toys manufactures and distributes a number of products to retailers. One of these products, Playclay, requires three pounds of material A$135$ in the manufacture of each unit. The company is now planning raw materials needs for the third quarter July, August, and September. Peak sales of Playclay occur in the third quarter of each year. To keep production and shipments moving smoothly, the company has the following inventory requirements:a$.$ The finished goods inventory on hand at the end of each month must be equal to $5,000$ units plus $30\%$ of the next months sales. The finished goods inventory on June $30$ is budgeted to be $17,000$ units.