Venture Systems is a consulting firm that develops e-commerce systems and Web sites for its clients. It has six available consultants and eight client projects under contract. The consultants have different technical abilities and experience, and as a result, the company charges different hourly rates for its services. Also, the consultants' skills are more suited for some projects than others, and clients sometimes prefer some consultants over others. The suitability of a consultant for a project is rated according to a 5-point scale, in which 1 is the worst and 5 is the best. The following table shows the rating for each consultant for each project, as well as the hours available for each consultant and the contracted hours and maximum budget for each project.

The company wants to know how many hours to assign each consultant to each project in order to best utilize the consultants€™ skills while meeting the clients€™ needs.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
c. If the company€™s objective is to maximize revenue while ignoring client preferences and consultant compatibility, will this change the solution in(b)?

Project Hourly Available Consultant Rate 1 2 345 6 7 8 Hours $155 140 165 300 270 150 3 3 33450 5 5 33 600 2 53 500 2 2 5300 2 33 710 3 5 4 3860 Project Hours 500 240 400 475 350 460 290 200 Contract Budget ($1,000s) 100 80 120 90 5 85 50 55