A small magazine publisher wants to determine the best combination of two possible magazines to print for the month of July. Backyard magazine, which he has published for years, is a steady seller. The publisher wants to make sure he prints at least 400 copies to meet his demand from the newsstands. Porch is a new venture, and has received the benefit of a great deal of advance publicity. The publisher is hoping that by positioning it near Backyard he will pick up some spill over demand from his regular readers. Also, he is hoping that the advertising campaign will bring in a new type of reader from a potentially very lucrative market. He wants to print at least 300 copies of Porch. The cover price for Backyard is $3.50; he is pricing Porch at $4.50, because of the magazines in this market seem to be able to command a higher price. The publisher has 50 hours of printing time available for this production run. He also has 30 hours in the collation department, where the magazines are actually assembled. Backyard requires 2.5 minutes per copy to print and 1.8 minutes per copy to collage. Because of its larger size, Porch will require 3 minutes to print and 2 minutes to collate. The publisher wants to maximize his revenues.
a. What is the publisher trying to optimize? Is he trying to maximize or minimize?
b. Write the objective function to support this analysis.
c. What inputs do you need to support your analysis?
d. Is there any extraneous data you have been given that you will not need?
e. What criteria has the publisher given you to support the analysis?
f. Create a spreadsheet model that supports your analysis.
g. Look carefully at your criteria. Surplus time is when you have extra time that is not being used. Is all of the printing time being used?
What about the collation time? Describe what this may mean to you as the publisher.