Problem:
Dr. Phil, a well-known TV talk show host and the most caring person in the U.S., cares about making as much money as possible. Besides his Oprah-like TV show, he sells books, videos, board games and Pick-Me-Up-I-Feel-Down™ snacks. Books sell for $22, board games for $34, the snacks at $2 per dozen, and videos for $30. Each of these products is sold at twice its costs. Books require 2 pounds of material per book, 1 cubic foot of space (Dr. Phil writes a lot), and 2 hours of assembly (they are made by hand). Videos require 0.5 cubic feet of space, 1 pound of material, and 1 hour of assembly. Board games need 3 pounds of material, 4 cubic feet of space, and 4 hours of assembly. Finally, the snacks require 5 cubic feet of space per dozen, 3 hours of assembly per dozen, and 2 pounds of material. Dr. Phil has limited resources. He only has 300 pounds of materials, 1000 cubic feet of storage space, and 500 hours of assembly time. For some emotional reason having to do with his mother, Dr. Phil does not want to make more than 30 but at least 24 books. Based on a recommendation from Dr. Frank, he retains you as a consultant. Feel Dr. Phil’s pain by answering the questions below showing all work.
a) Summarize the above information in a useful table.
b) What are the decision variables? Pick a logical symbol for each one.
c) What is the objective function? Is this a maximization or a minimization problem?
d) What are ALL of the constraint equations?
e) It turns out that marketing vastly underestimated the price that they can sell Dr. Phil’s Pick-Me-Up-I-Feel-Down™ snacks. If you had solved the above problem with a LP program, such as available with Excel, and had all of the information that it would provide, what information would you use and how would you use it? Use the applicable terms that we have learned.