In the realm of financial reporting, companies engage in a meticulous process to ensure accurate representation of their financial health. Consider a fictitious company, Tech Solutions Inc., a software development firm, which operates on a calendar year basis. Tech Solutions Inc. has provided you with the following information for the year ended December 31, 2023:

• Sales Revenue: $2,500,000
• Cost of Goods Sold: $800,000
• Operating Expenses: $500,000
• Interest Expense: $20,000
• Dividend Revenue: $10,000
• Gain on Sale of Equipment: $15,000
• Loss from Lawsuit Settlement: $25,000
• Income Tax Rate: 30%

Based on the provided data, you are required to perform the following tasks:

1. Prepare an income statement for Tech Solutions Inc. for the year ended December 31, 2023, following the multiple-step format, including gross profit, operating income, and net income.
2. Calculate the gross profit margin and the operating profit margin for Tech Solutions Inc.
3. Determine the company's net income after tax.
4. Record the closing entries for the company, assuming that Tech Solutions Inc. uses a periodic inventory system and closes all revenue and expense accounts at the end of the accounting period.
5. Provide the journal entries required to adjust for the gain on sale of equipment and the loss from lawsuit settlement, assuming they were not previously recorded.

Ensure that your responses are presented in a clear and organized manner, demonstrating a comprehensive understanding of the income statement preparation process, financial statement analysis, and the adjustment and closing procedures within the accounting cycle.