Statistics-Premier Consulting’s two consultants, Avery and Baker

1. Premier Consulting’s two consultants, Avery and Baker, can be
scheduled to work for clients up to a maximum of 160 hours each over the next
four weeks. A third consultant, Campbell, has some administrative assignments
already planned and is available for clients up to a maximum of 140 hours over
the next four weeks. The company has four clients with projects in process. The
estimated hourly requirements for each of the clients over the four-week period
are as follows:

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:

b. Formulate the problem as a linear program,
with the optimal solution providing the hours each consultant should be
scheduled for each client to maximize the consulting firm’s billings. What is
the schedule and what is the total billing?

c. New information shows that Avery doesn’t have the experience
to be scheduled for client B. If this consulting assignment is not permitted,
what impact does it have on total billings? What is the revised schedule?

2. A local television station plans to drop four Friday evening
programs at the end of the season. Steve Botuchis, the station manager,
developed a list of six potential replacement programs. Estimates of the
advertising revenue ($) that can be expected for each of the new programs in
the four vacated time slots are as follows. Mr. Botuchis asked you to find the
assignment of programs to time slots that will maximize total advertising
revenue.