d). Due to unforeseen circumstances, Ben becomes unavailable for Project 2. Considering this constraint, revise the linear programming model, and find the new optimal assignment and total billing.

Alpha Consulting is a professional services firm that provides specialized expertise to its clients. They have three consultants: Alice, Ben, and Claire. These consultants have varying availability and skill sets, and the company needs to assign them to different client projects to maximize their billings. The company has identified four potential projects with different requirements and profitability. Consultant Availability: - Alice: Available for a maximum of 160 hours - Ben: Available for a maximum of 160 hours - Claire: Available for a maximum of 140 hours Project Requirements: - Project W: Requires 180 hours of work. - Project X: Requires 75 hours of work. - Project Y: Requires 100 hours of work. - Project Z: Requires 85 hours of work. Hourly rates vary for the consultant-client combination and are based on several factors, including project type and the consultant's experience. The rates (dollars per hour) for each consultant-client combination are as follows: Now a) Develop a network representation of the problem. b) Develop a linear programming model to determine the optimal assignment of consultants to projects, maximizing Alpha Consulting's total billing. Define the decision variables, objective function, and constraints. c) Solve the linear programming model using an appropriate solver or method of your choice. Determine the optimal assignment of consultants to projects and calculate the total billing. Alpha Consulting is a professional services firm that provides specialized expertise to its clients. They have three consultants: Alice, Ben, and Claire. These consultants have varying availability and skill sets, and the company needs to assign them to different client projects to maximize their billings. The company has identified four potential projects with different requirements and profitability. Consultant Availability: - Alice: Available for a maximum of 160 hours - Ben: Available for a maximum of 160 hours - Claire: Available for a maximum of 140 hours Project Requirements: - Project W: Requires 180 hours of work. - Project X: Requires 75 hours of work. - Project Y: Requires 100 hours of work. - Project Z: Requires 85 hours of work. Hourly rates vary for the consultant-client combination and are based on several factors, including project type and the consultant's experience. The rates (dollars per hour) for each consultant-client combination are as follows: Now a) Develop a network representation of the problem. b) Develop a linear programming model to determine the optimal assignment of consultants to projects, maximizing Alpha Consulting's total billing. Define the decision variables, objective function, and constraints. c) Solve the linear programming model using an appropriate solver or method of your choice. Determine the optimal assignment of consultants to projects and calculate the total billing