SilComputers makes quarterly decisions about their product mix. While their full product line includes hundreds of products, we will consider a simpler problem with just two products: notebook computers and desktop computers. SilComputers would like to know how many of each product to produce in order to maximize profit for the quarter.
There are a number of limits on what SilComputers can produce. The major constraints are as follows:
Given current market conditions, material cost, and our production system, each notebook computer produced generates $750 profit, and each desktop produces $1000 profit.
There are many questions SilComputer might ask. The most obvious are such things as ``How many of each type computer should SilComputer produce in the next quarter?'' ``What is the maximum profit SilComputer can make?'' Less obvious, but perhaps of more managerial interest are ``How much should SilComputer be willing to pay for an extra memory chip set?'' ``What is the effect of losing 1,000 minutes of assembly time due to an unexpected machine failure?'' ``How much profit would we need to make on a 32MB notebook computer to justify its production?''
Linear programming gives us a mechanism for answering all of these questions quickly and easily. There are three steps in applying linear programming: modeling, solving, and interpreting.