The budget officer of Sux Company Limited is preparing the budget for the fiscal year of $2023.$ The cost of goods sold for December $2022$ was $$1,500,000$ while the gross profit was $$500,000.$ The company anticipates that the sales of the company would grow at $2$ percent for the first quarter of $2023,3\%$ for the second quarter of $2023,4\%$ for the third quarter, and $5\%$ for the last quarter of $2023.$ The units of production for December $2022$ was $1,000,000$ units. For each product sold, the company uses $2$ units of raw materials, $1\mathrm{.}5$ hours of direct labour. Overheads are $80$ percent of direct labour costs. The company receives $20$ percent of its sales in the month of sales, $40$ percent in a month$$s time, and the remaining balance two months after sales. The company pays workers their wages in the month they provide their service. The company$$s suppliers offer it one month of credit to pay for raw materials purchased. The average unit price of the raw materials supplied is $$0\mathrm{.}20.$ The company$$s cash balance at the end of December $2022$ was $$100,000.$

Required:

a$.$ Prepare the sales budget for $2023.(5$ marks$)$

b$.$ Prepare the production budget for $2023.(5$ marks$)$

c$.$ Prepare the manufacturing budget for $2023.(5$ marks$)$

d$.$ Prepare the cash budget and determine whether the company needs additional finance or not $(5$ marks$)$