Ben Johnson is the manager of the jewelry department of a large chain of department stores. The department store has succeeded on the basis of customer service and quality of merchandise. As a manager, Ben is compensated with a salary of $$340,000$ and a bonus based on his unit$$s operating income. The bonus pool is $10\%$ of company$-$wide operating income. When the unit$$s return on invested assets exceeds the rate of return of the whole company, the unit manager is included in the bonus pool, which is divided evenly among the managers who qualify for the bonus. In the current period, $25$ managers qualified for the bonus, including Ben.

Jewelry Department Whole Company

Stock price $ $45$

Operating income $ $2,038,000$ $ $17,900,000$

Assets invested $ $23,900,000$ $ $288,900,000$

Customer service $45$

Quality of service $48$

Total revenue $ $3,640,000$ $ $125,000,000$

Required:

Based on the above information, what is the amount of total compensation for Ben?

multiple choice

$$340,000$

$$414,350$

$$411,600$

$$423,600$