Let's evaluate each option:a$.$ Variable costs change in proportion to changes in the related level of activity while fixed costs remain unchanged irrespective of the level of activity within the relevant range.This statement is correct. Variable costs fluctuate with activity levels, while fixed costs remain constant within a certain range of activity.b$.$ Variable costs include costs of materials and factory wages while fixed costs include salaries paid to office staff.This statement is correct. Variable costs typically include direct materials and direct labor, while fixed costs often include salaries for administrative staff.c$.$ Variable costs remain variable throughout the production period and fixed costs remain fixed at all times.This statement is incorrect. While variable costs do change with activity levels, fixed costs can change if the relevant range is exceeded or if there are changes in business operations.d$.$ Variable costs can be reduced by reducing the level of activity while fixed cost cannot be reduced even if the level of activity is reduced.This statement is correct. Reducing activity levels will reduce variable costs, but fixed costs remain constant within the relevant range.The correct answer is c$.$ Variable costs remain variable throughout the production period and fixed costs remain fixed at all times.