GuruJi Inc is considering different projects for the next year in order to increase its capacity by at least 100,000 units. It has an option to choose between six different projects. The NPVs and capacities for different projects are given below:

Project	NPV (in $)	Capacity (units)
1	100,000	10,000
2	300,000	40,000
3	250,000	50,000
4	200,000	25,000
5	350,000	30,000
6	100,000	15,000

Also, the following conditions must be met:

At least one project from 1, 2, and 3 must be selected.

At least one project from 4, 5, and 6 must be selected.

If 1 and 2 are selected then 3 cannot be selected

If 2 is selected then 5 cannot be selected.

If 4 is selected then 6 must be selected and vice versa.

Formulate an integer linear programming problem clearly defining the variables to maximize the NPV.

Use Solver to find the optimal solution.

Which projects should they select?

What is the expected NPV?