The Lancaster Decor Company (LDC) makes wallpaper. One of its factories makes two types of wallpaper, pasted and unpasted. Both types of wallpaper are printed by a high quality gravure process and both are packed at the same Packaging plant. The difference is that the pasted wallpaper must pass through a pasting process before it is packed. The production planner wishes to know how many of each to produce next week so as to maximize the expected gross profit. In the case of pasted, this is $0.90 per yard and is $0.75 per yard for unpasted. There are constraints on the production facilities that will affect the planner's freedom of action. The factory has the print capacity to produce 50 yards per minute of either type of wallpaper, and the printer is available for 40 hours during the week. The capacity of the Packaging plant is measured in ''Packaging units'', of which there are 300,000 available. A Packaging unit is the length in yards of so-called standard wallpaper (which is no longer made by LDC). Pasted wallpaper is three times as thick as standard and unpasted is twice as thick as standard, the adhesive accounting for the difference. Thus, it takes three times as long to pack a roll of pasted wallpaper, compared with a roll of standard wallpaper. The pasting plant has a capacity of 100,000 yards per week. The Marketing Department insists that the factory must produce at least 30,000 yards of each type of wallpaper.
See explanation in the Excel.
First, we assume the following decision variables
x1-yards of pasted wallpaper
x2-yards of ...
Linear programming for the Lancaster Decor Company is examined in the solution.