SunNet is a residential Internet Service Provider $($ISP$)$ in the central Florida area. Presently, the company operates one centralized facility that all of its clients call into for Internet access. To improve service, the company is planning to open three satellite offices in the cities of Pine Hills, Eustis, and Sanford. The company has identified five different regions to be serviced by these three offices. The following table summarizes the number of customers in each region, the service capacity at each

$214$

Chapter $5$ Network Modeling

office, and the average monthly per customer cost of providing service to each region from each office. Table entries of $"$n$.$a$."$ indicate infeasible region$-$to$-$servicecenter combinations. SunNet would like to determine how many customers from each region to assign to each service center to minimize cost.

$\backslash$table$[[$Region$,$Pine Hills,Eustis,Sanford,Customers$],[1,$$$6\mathrm{.}50,$$$7\mathrm{.}50,$n$.$a$.,30,000],[2,$$$7\mathrm{.}00,$$$8\mathrm{.}00,$n$.$a$.,40,000],[3,$$$8\mathrm{.}25,$$$7\mathrm{.}25,$$$6\mathrm{.}75,25,000],[4,$n$.$a$.,$$$7\mathrm{.}75,$$$7\mathrm{.}00,35,000],[5,$n$.$a$.,$$$7\mathrm{.}50,$$$6\mathrm{.}75,33,000],[$Capacity$,60,000,70,000,40,000,]]$

a$.$ Draw a network flow model to represent this problem.

b$.$ Implement your model in Excel and solve it$.$

c$.$ What is the optimal solution?