A company has identified a number of promising projects. The cash flows $($with unit $$1000)$ for the first two years are

shown in the following table.

The company managers have decided that they can allocate up to $$250,000$ in each of the first $2$ years to fund these

projects. If less than $$250,000$ is used the first year, the balance can be invested at $10\%$ and used to augment the

next year's budget. What is the optimal set of investment and the corresponding profit $($net present value$)?$

What are decision variables?

What is the objective function?

What are constraints?