m. Thus, if the cost of one MSC is M, then we would like to use a proportional-cost model and to say that the MSC cost per cell is M/200. However, there is an offset factor, a fixed cost of MSCs, that is analogous to mailing letters. When you mail a letter in most countries, there is some charge for the first unit weight, and then there is a subsequent charge for each unit above the first unit. Let us assume a rate of 30 cents for the first ounce and 20 cents for each ounce beyond that.2 We can graph the postage charge as a function of weight as in Fig. 46.1. We pay the full cost of each ounce even when we use only a fraction of that ounce. Sometimes we can use a linear approximation of the postage function, as shown in Fig. 46.2. The diagonal line is a linear representation that smoothes out the step function of the postage rate. The linear representation charges us 20 cents to mail a letter and 20 cents per ounce. If we have a collection of letters all the same weight, then we use the ex- act step function to calculate the postage for them. However, if we have a collection of let- ters of varying weight, then we can estimate the cost by weighing the entire pile and us- ing 20 cents per letter plus 20 cents per ounce as a good estimate of the total postage cost. If one MSC serves 200 base stations, then we can use a similar approximation for the MSC cost of a growing system. The MSC cost step function is M for the first 200 cells and M for each 200 cells after that. The linear approximation is M/2 plus M/200 for each cell. In fact, the actual cost of an MSC increases with the number of cells it is serv- ing, so the MSC cost function has steps that are rising up to the maximum of 200 cells. Figure 46.3 shows this step function and its linear approximation. This linear approximation to a step function is only useful when we are using multi- ple steps. If we are planning a system that is never going to grow beyond a single MSC, 2The United States Postal Service still uses ounces for weight, where 1 ounce is 28.3 gr