A common capital budgeting decision involves selecting from a set of possible projects when budget limitations make it impossible to select all of these. A separate $0-1$ variable can be defined for each project. We will see this in the following example.

Quemo Chemical Company is considering three possible improvement projects for its plant: a new catalytic converter, a new software program for controlling operations, and expanding the warehouse used for storage. Capital requirements and budget limitations in the next two years prevent the firm from undertaking all of these at this time. The net present value $($the future value of the project discounted back to the present time$)$ of each of the projects, the capital requirements, and the available funds for the next two years are as under.

Project NPV Year $1$ Year $2$

Catalytic Converter $$25,000$ $$8000$ $$7000$

Software $$18,000$ $$6000$ $$4000$

Warehouse Expansion $$32,000$ $$12,000$ $$8000$

Available Fund $$20,000$ $$16,000$

To formulate this as Linear programming problem,