Linear Algebra: Find bases for the kernel and range for the linear transformation T:R^3 to R^2 defined by T(x1, x2, x3) = (x1+x2, -2x1+x2-x3). We solve by finding the corresponding 2 x 3 matrix A, and find its null space and column span.
Several types of expenses affect profits for a business including equipment costs, inventory and facilities costs. There are two main categories for all business expenses: operating expenses and overhead expenses. The costs that fall into each category depend on the nature of the business. Essentially, operating expenses are directly related to production, while overhead expenses are the costs to run the business. Operating expenses include materials, labor and machinery used to make a product or deliver a service. For example, a soda bottler has the cost of aluminum for cans, machinery costs and labor costs.
All field employee labor and burden costs of those who are not working on the jobs under construction (such as during slow times or downtime) should be included as well, and field vehicles and field equipment expenses when they are not being used on jobs should be included. Overhead must not include items used to build projects in the field. Instead, these items should be included in your bid estimate and charged to job costs. Examples of these items include all field personnel and related expenses, all field vehicles and related expenses, tools and liability insurance premiums based on job costs.