Final answer:
Committed fixed costs remain constant irrespective of production levels, and are associated with long-term investments. Discretionary fixed costs also remain constant and are subject to change by management decisions, but do not vary directly with production levels. Option 4 is the correct choice.
Step-by-step explanation:
The classification of committed fixed costs and discretionary fixed costs involves understanding how these costs behave with respect to the level of production. Committed fixed costs are those costs that a business has an obligation to pay, often associated with long-term investments such as leases, salaries of key personnel, and depreciation on equipment. These costs remain constant and do not vary with production levels. On the other hand, discretionary fixed costs are those that can be altered in the short term by current managerial decisions without having a significant impact on the firm's ability to operate, such as advertising, research and development, and public relations. These costs can be changed in the short run and are not directly tied to the level of production.
Therefore, among the given options, the correct classification of a committed fixed cost and a discretionary fixed cost is represented by Option 4: Both committed and discretionary fixed costs remain constant and do not vary with the level of production.