Vantage 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 their services. Also, the consultants€™ skills are more suited for some projects than for others, and clients sometimes prefer some consultants over others. The suitability of a consultant for a project is rated according to a five-point scale, where 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 that will best utilize the consultants€™ skills while meeting the clients€™ needs.
a. Formulate and solve a linear programming model for this problem.
b. If the company€™s objective is to maximize revenue while ignoring client preferences and consultant compatibility, will this change the solution in(b)?

Hourly Available Consultant Rate 1 2 35 6 7 8 Hours A $155 3 3 5 5 3 33 3 450 B 140 3 3 7 5 5 5 33 600 C 165 2 1 3 3 2 1 5 3 500 D 300 1 3 11 2 2 51 300 270 3 1 1 2 2 1 33 710 F 150 45 3 2 3 5 43 860 Project Hour Contract Budget $1000s) 500 240 400 475 350 460 290 200 100 80 120 90 65 85 50 55