Budgeting

AXO Pte Ltd is a company based in Singapore that produces a single product.
Shown below are the agreed budgeted sales for the product for May to October 2022.
May – 16,000 units
June – 16,000 Units
July – 22,000 Units
August – 17,000 Units
September – 20,000 Units
October – 24,000 Units

The company policy is that at each month end, the closing inventory of finished goods should be 25% of the following months forecast sales and the inventory of direct material should be sufficient for 10% of the following month’s production. One unit of raw material makes one unit of finished goods and there is no wastage.
Raw material purchases are paid for during the month following the month of purchase. All other expenses are paid for as incurred. All sales are made on credit and the company expects cash receipts for 50% of sales in the month of sale and 50% in the following month.
The company operates an absorption costing system which is computed on a monthly basis. This cost is used to place a value on the inventory holding. Opening inventory is valued at the unit cost which was established in the previous month. At 1st June 2022 finished inventory should be assumed $40 per unit. A flow of cost based on FIFO is assumed.
Sales are made at a price of $58 per unit.
Estimated costs to be used in the budget preparation for the product are:
Manufacturing costs:
Material $10.00 per unit produced
variable overhead and labour $16.00 per unit produced
Fixed overhead costs $210,000 per month
(Including depreciation of $54,000 per month)
Selling costs:
Variable $7.00 per unit sold
Fixed $164,000 per month
2
Each month a monthly cost control report is sent to the department manager, a copy of which is also passed to the director who controls a number of departments. the budgets are set by the director and the managers are not consulted over the budget or the use of the monthly control report.
In the recent month as a result of the report, the director sent a memo to the manager of the Production Department pointing out that the department must spend within its funding limits and that any spending more than 3% above budget on any item would not be tolerated. Upon reviewing the Performance Report of the production department, you also noticed that the budget was based on 10,000 units but in fact 15,000 units were produced.
You work as the Management Accountant of the company. The Director has requested your assistance in reviewing the current budgetary and control system.
Required:
(a) Compute the monthly budgeted production and material purchases for June to September 2022 in units.

My questions: How do I calculate the Closing inventory for Oct in order for me to calculate the closing inventory for the purchase budget?