Final answer:
Option D, which involves relaxing credit terms and giving customers more time to pay, would lengthen the operating cycle of a business because it delays the conversion of sales into cash.
Step-by-step explanation:
The question asks which of the following options would lengthen the operating cycle of a business. An operating cycle refers to the amount of time it takes for a company to purchase inventory, sell the products, and collect cash from customers. This cycle plays a critical role in determining company's liquidity and working capital management.
Option A, Faster collection of accounts receivables, would actually shorten the operating cycle, as the company is able to convert sales into cash more quickly. Similarly, Option B, Selling inventory in a shorter period of time, would also result in a shorter operating cycle because the inventory is turned over more quickly.
Option C, Increasing the number of customers who paid cash, would likewise not lengthen the operating cycle, because it would lead to immediate cash receipts from sales, thereby shortening the cycle.
Option D, Relaxing credit terms and allowing customers more time to pay, would lengthen the operating cycle because it would take longer to convert sales into cash. This is because customers are given more time to make their payments.
Therefore, the mention correct option answer that lengthens the operating cycle is Option D.