In this section we will examine how problem formulation can be made more realistic by incorporating constraints. Because the relationships we will be dealing with will all be linear, the constraints can be identified as areas on the straight line graphs.
Here's a problem
A computer networking company installs 2 types of network; the Type A Network and Type B Network. The Type A network is only an intranet which has no connections to the outside world. The Type B network has connections to the internet, and so requires more skilled engineers to install because of the security considerations.There are 2 types of network engineer, referred to as highly skilled and semi-skilled.
The following table indicates how many hours of each labor type are required to install the Type A network and the Type B network. In addition, the profit from each installation is indicated. Type B networks provide a higher profit (1200, vs. 1000) but they require more skilled labor hours.
Table 2: Labor mix for network installation
Highly skilled Semi-skilled Profit Network A 10 50 1000 Network B 40 30 1200
The practical issue is that there is always a small pool of skilled labor to draw from, for this company in this particular month there are 800 hours of skilled labor and 3000 hours of semi-skilled labor available.
The decision problem here is:
How many of each network should the company install to maximize profit?