What is the salesperson doing when, after his presentation is over, he asks, "May I call the company and place your order for 20 cases of Ecco brand golfing shoes?"

trying to close the sale

Explanation:

When someone is closing a sale, he/she is trying the complete the sales process by effectively getting a purchase order. In this case, the salesperson is trying to convince the client to finally place an order for 20 cases of Ecco brand golfing shoes. The whole selling process is carried out to finally be able to close the sale, it is the climax of the sales process, the salesperson either makes it or not.