The correct answer is: The cook will be cooking food at this time tomorrow.
The word “shall” is used to express a strong obligation or necessity. In this case, there is no strong obligation or necessity for the cook to be cooking food at this time tomorrow. Therefore, the word “shall” is not the correct answer.
The word “will” is used to express a future event that is likely to happen. In this case, it is likely that the cook will be cooking food at this time tomorrow. Therefore, the word “will” is the correct answer.
The word “should” is used to express a recommendation or suggestion. In this case, there is no recommendation or suggestion that the cook should be cooking food at this time tomorrow. Therefore, the word “should” is not the correct answer.
The word “may” is used to express possibility or permission. In this case, it is possible that the cook may be cooking food at this time tomorrow. However, there is no permission for the cook to be cooking food at this time tomorrow. Therefore, the word “may” is not the correct answer.