Question 2:

As the manager of a technology department, you have the responsibility to select the most beneficial combination of four software development projects to maximize the department's overall productivity while staying within budget. Each project is represented by a binary decision variable, indicating whether it's chosen (1) or not chosen (0). Additionally, you have constraints on budget and team availability.

The potential benefits (in units of productivity), required team effort (in person-weeks), and associated costs (in thousands of dollars) for each project are as follows:

Project A: Benefit = 30 units, Team Effort = 4 person-weeks, Cost = $10,000

Project B: Benefit = 20 units, Team Effort = 2 person-weeks, Cost = $6,000

Project C: Benefit = 40 units, Team Effort = 5 person-weeks, Cost = $12,000

Project D: Benefit = 25 units, Team Effort = 3 person-weeks, Cost = $8,000

You have a budget constraint of $30,000 and a team availability constraint of 10 person-weeks. Additionally, due to the interdependencies of projects, you cannot select both Project A and Project D simultaneously.

Formulate this as a binary linear optimization problem to find the optimal combination of projects that maximize overall productivity while adhering to the constraints. Please include the decision variables, objective function, and all constraints, and solve the problem using a solver.

PLEASE INCLUDE STEP BY STEP DIRECTIONS FOR CALCULATIONS AND CONSTRAINTS USING THE SOLVER TOOL ON EXCEL