Introductory Example

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:

1. Each computer (either notebook or desktop) requires a Processing Chip. Due to tightness in the market, our supplier has allocated 10,000 such chips to us.
2. Each computer requires memory. Memory comes in 16MB chip sets. A notebook computer has 16MB memory installed (so needs 1 chip set) while a desktop computer has 32MB (so requires 2 chip sets). We received a great deal on chip sets, so have a stock of 15,000 chip sets to use over the next quarter.
3. Each computer requires assembly time. Due to tight tolerances, a notebook computer takes more time to assemble: 4 minutes versus 3 minutes for a desktop. There are 25,000 minutes of assembly time available in the next quarter.

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.

• Modeling
• Solving the Model
• Using Solver