40 To satisfy telecommunication needs for the next 20 years, Telstar Corporation estimates that the number of circuits required between the United States and Germany, France, Switzerland, and the United Kingdom will be as given in Table 45.

Two types of circuits may be created: cable and satellite.

Two types of cable circuits (TA7 and TA8) are available.

The fixed cost of building each type of cable and the circuit capacity of each type are as given in Table 46.

TA7 and TA8 cable go underseas from the United States to the English Channel. Thus, it costs an additional amount to extend these circuits to other European countries. The annual variable cost per circuit is given in Table 47.

To create and use a satellite circuit, Telstar must launch a satellite, and each country using the satellite must have an earth station(s) to receive the signal. It costs $3 billion to launch a satellite. Each launched satellite can handle up to 140,000 circuits. All earth stations have a maximum capacity of 190 circuits and cost $6,000 per year to operate. Formulate an integer programming model to help determine how to supply the needed circuits and minimize total cost incurred during the next 20 years.
Then use LINDO (or LINGO) to find a near optimal solution. LINDO after 300 pivots did not think it had an optimal solution! By the way, do not require that the number of cable or satellite circuits in a country be integers, or your model will never get solved! For some variables, however, the integer requirement is vital!†

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TABLE 45 Country Required Circuits France 20,000 Germany 60,000 Switzerland 16,000 United Kingdom 60,000 TABLE 46 Cable Type Fixed Operating Cost ($ Billion) Capacity TA7 TA8 1.6 8,500 2.3 37,800 TABLE 47 Country Variable Cost per Circuit ($) France 0 Germany 310 Switzerland 290 United Kingdom 0