Answer:
No, I do not agree with the CEO.
Sunk cost is the one which is incurred in past and cannot be avoided now, and thus, not involved in any decision making.
Further it is not regularly incurring cost.
A company shall operate till the time the company is able to recover its variable costs.
Here the company is recovering the entire variable cost as the fixed cost = $40,000, and losses are $30,000
That means $40,000 - $30,000 = $10,000 is the amount after meeting the variable cost the company recovers as part of fixed cost.
If a company can meet its variable cost, it shall not shut down. Therefore, CEO's decision is wrong.